Kurse
Ãœber Sowiso
Kontakt
Freischalten 
English
Kurse
Ãœber Sowiso
Kontakt
Freischalten 
English
Linear Algebra
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Kursinhalt
Complex numbers
Introduction to Complex numbers
THEORIE
T
1.
Imaginary numbers
ÃœBUNG
Ã
2.
Imaginary numbers
7
THEORIE
T
3.
The notion of complex numbers
ÃœBUNG
Ã
4.
The notion of complex numbers
12
THEORIE
T
5.
Polar coordinates
ÃœBUNG
Ã
6.
Polar coordinates
7
THEORIE
T
7.
Real and imaginary part
ÃœBUNG
Ã
8.
Real and imaginary part
5
Calculating with complex numbers
THEORIE
T
1.
Calculating with polar coordinates
ÃœBUNG
Ã
2.
Calculating with polar coordinates
Kompletten Zugriff freischalten locked
THEORIE
T
3.
The quotient
ÃœBUNG
Ã
4.
The quotient
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Complex conjugate
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Complex conjugate
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Geometric interpretation
ÃœBUNG
Ã
8.
Geometric interpretation
Kompletten Zugriff freischalten locked
Complex functions
THEORIE
T
1.
Complex exponents
ÃœBUNG
Ã
2.
Complex exponents
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Rules of calculation for complex powers
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
4.
Rules of calculation for complex powers
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Complex sine and cosine
ÃœBUNG
Ã
6.
Complex sine and cosine
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Complex logarithm
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Complex logarithm
Kompletten Zugriff freischalten locked
Complex polynomials
THEORIE
T
1.
The notion of a complex polynomial
ÃœBUNG
Ã
2.
The notion of a complex polynomial
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Factorization of complex polynomials
ÃœBUNG
Ã
4.
Factorization of complex polynomials
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Zeros of complex polynomials
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Zeros of complex polynomials
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Fundamental theorem of algebra
ÃœBUNG
Ã
8.
Fundamental theorem of algebra
Kompletten Zugriff freischalten locked
THEORIE
T
9.
Real polynomials
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
10.
Real polynomials
Kompletten Zugriff freischalten locked
Conclusion of Complex numbers
THEORIE
T
1.
End of Complex numbers
Differential equations and Laplace transforms
THEORIE
T
1.
The Laplace transform
ÃœBUNG
Ã
2.
The Laplace transform
6
THEORIE
T
3.
The inverse Laplace transform
ÃœBUNG
Ã
4.
The inverse Laplace transform
8
THEORIE
T
5.
Laplace transforms of differential equations
ÃœBUNG
Ã
6.
Laplace transforms of differential equations
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Convolution
ÃœBUNG
Ã
8.
Convolution
Kompletten Zugriff freischalten locked
THEORIE
T
9.
Laplace transforms of Heaviside functions
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
10.
Laplace transforms of Heaviside functions
Kompletten Zugriff freischalten locked
THEORIE
T
11.
Laplace transforms of periodic functions
ÃœBUNG
Ã
12.
Laplace transforms of periodic functions
Kompletten Zugriff freischalten locked
THEORIE
T
13.
Riemann-Stieltjes integration
Kompletten Zugriff freischalten locked
THEORIE
T
14.
Laplace transforms of delta functions
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
15.
Laplace transforms of delta functions
Kompletten Zugriff freischalten locked
THEORIE
T
16.
Transfer and response functions
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
17.
Transfer and response functions
Kompletten Zugriff freischalten locked
Vector calculus in plane and space
Vectors in Planes and Space
THEORIE
T
1.
The notion of vector
ÃœBUNG
Ã
2.
The notion of vector
9
THEORIE
T
3.
Scalar multiplication
ÃœBUNG
Ã
4.
Scalar multiplication
6
THEORIE
T
5.
Addition of vectors
ÃœBUNG
Ã
6.
Addition of vectors
6
THEORIE
T
7.
Linear combinations of vectors
ÃœBUNG
Ã
8.
Linear combinations of vectors
8
Straight Lines and Planes
THEORIE
T
1.
Straight lines and planes
ÃœBUNG
Ã
2.
Straight lines and planes
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Parametrization of a plane
ÃœBUNG
Ã
4.
Parametrization of a plane
Kompletten Zugriff freischalten locked
Bases, Coordinates and Equations
THEORIE
T
1.
The notion of basis
ÃœBUNG
Ã
2.
The notion of basis
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Coordinate space
ÃœBUNG
Ã
4.
Coordinate space
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Straight lines in the plane in coordinates
ÃœBUNG
Ã
6.
Straight lines in the plane in coordinates
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Planes in coordinate space
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Planes in coordinate space
Kompletten Zugriff freischalten locked
THEORIE
T
9.
Lines in the coordinate space
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
10.
Lines in the coordinate space
Kompletten Zugriff freischalten locked
Distances, Angles and Inner Product
THEORIE
T
1.
Distances, angles, and dot products
ÃœBUNG
Ã
2.
Distances, angles, and dot products
9
THEORIE
T
3.
Dot product
ÃœBUNG
Ã
4.
Dot product
5
THEORIE
T
5.
Properties of the dot product
ÃœBUNG
Ã
6.
Properties of the dot product
Kompletten Zugriff freischalten locked
THEORIE
T
7.
The standard dot product
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
The standard dot product
Kompletten Zugriff freischalten locked
THEORIE
T
9.
Normal vectors
ÃœBUNG
Ã
10.
Normal vectors
Kompletten Zugriff freischalten locked
The Cross Product
THEORIE
T
1.
Cross product in 3 dimensions
ÃœBUNG
Ã
2.
Cross product in 3 dimensions
Kompletten Zugriff freischalten locked
THEORIE
T
3.
The concept of volume in space
ÃœBUNG
Ã
4.
The concept of volume in space
Kompletten Zugriff freischalten locked
THEORIE
T
5.
The volume of a parallelepiped
ÃœBUNG
Ã
6.
The volume of a parallelepiped
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Properties of the cross product
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Properties of the cross product
Kompletten Zugriff freischalten locked
THEORIE
T
9.
The standard cross product
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
10.
The standard cross product
Kompletten Zugriff freischalten locked
Conclusion of Vector calculus in plane and space
THEORIE
T
1.
End of Vector calculus in plane and space
Systems of linear equations and matrices
Linear equations
THEORIE
T
1.
The notion of linear equation
ÃœBUNG
Ã
2.
The notion of linear equation
5
THEORIE
T
3.
Reduction to a base form
ÃœBUNG
Ã
4.
Reduction to base form
2
THEORIE
T
5.
Solving a linear equation with a single unknown
ÃœBUNG
Ã
6.
Solving a linear equation with a single unknown
5
THEORIE
T
7.
Solving a linear equation with several unknowns
ÃœBUNG
Ã
8.
Solving a linear equation with several unkowns
Kompletten Zugriff freischalten locked
Systems of Linear Equations
THEORIE
T
1.
The notion of a system of linear equations
ÃœBUNG
Ã
2.
The notion of a system of linear equations
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Homogeneous and inhomogeneous systems
ÃœBUNG
Ã
4.
Homogeneous and inhomogeneous systems
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Lines in the plane
ÃœBUNG
Ã
6.
Lines in the plane
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Planes in space
ÃœBUNG
Ã
8.
Planes in space
Kompletten Zugriff freischalten locked
THEORIE
T
9.
Elementary operations on systems of linear equations
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
10.
Several linear equations with several unknowns
Kompletten Zugriff freischalten locked
Systems and matrices
THEORIE
T
1.
From systems to matrices
ÃœBUNG
Ã
2.
From systems to matrices
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Equations and matrices
ÃœBUNG
Ã
4.
Equations and matrices
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Echelon form and reduced echelon form
ÃœBUNG
Ã
6.
Echelon form and reduced echelon form
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Row reduction of a matrix
ÃœBUNG
Ã
8.
Row reduction of a matrix
Kompletten Zugriff freischalten locked
THEORIE
T
9.
Solving linear equations by Gaussian elimination
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
10.
Solving linear equations by Gaussian elimination
Kompletten Zugriff freischalten locked
THEORIE
T
11.
Solvability of systems of linear equations
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
12.
Solvability of systems of linear equations
Kompletten Zugriff freischalten locked
THEORIE
T
13.
Systems with a parameter
ÃœBUNG
Ã
14.
Systems with a parameter
Kompletten Zugriff freischalten locked
Matrices
THEORIE
T
1.
The notion of matrix
ÃœBUNG
Ã
2.
The notion of matrix
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Simple matrix operations
ÃœBUNG
Ã
4.
Simple matrix operations
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Multiplication of matrices
ÃœBUNG
Ã
6.
Multiplication of matrices
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Matrix equations
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Matrix equations
Kompletten Zugriff freischalten locked
THEORIE
T
9.
The inverse of a matrix
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
10.
The inverse of a matrix
Kompletten Zugriff freischalten locked
Conclusion of Systems of linear equations and matrices
THEORIE
T
1.
Applications of systems of linear equations
ÃœBUNG
Ã
2.
Applications of systems of linear equations
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Notes
Vector spaces
Vector spaces and linear subspaces
THEORIE
T
1.
The notion of vector space
ÃœBUNG
Ã
2.
The notion of vector space
6
THEORIE
T
3.
The notion of linear subspace
ÃœBUNG
Ã
4.
The notion of linear subspace
8
THEORIE
T
5.
Lines and planes
ÃœBUNG
Ã
6.
Lines and planes
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Affine subspaces
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Affine subspaces
Kompletten Zugriff freischalten locked
Spans
THEORIE
T
1.
Spanning sets
ÃœBUNG
Ã
2.
Spanning sets
8
THEORIE
T
3.
Operations with spanning vectors
ÃœBUNG
Ã
4.
Operations with spanning vectors
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Independence
ÃœBUNG
Ã
6.
Independence
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Basis and dimension
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Basis and dimension
Kompletten Zugriff freischalten locked
THEORIE
T
9.
Finding bases
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
10.
Finding bases
Kompletten Zugriff freischalten locked
More about subspaces
THEORIE
T
1.
Intersection and sum of linear subspaces
ÃœBUNG
Ã
2.
Intersection and sum of linear subspaces
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Direct sum of two linear subspaces
ÃœBUNG
Ã
4.
Direct sum of two linear subspaces
Kompletten Zugriff freischalten locked
Coordinates
THEORIE
T
1.
The notion of coordinates
ÃœBUNG
Ã
2.
The notion of coordinates
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Coordinates of sums of scalar multiples
ÃœBUNG
Ã
4.
Coordinates of sum and scalar multiples
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Basis and echelon form
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Basis and echelon form
Kompletten Zugriff freischalten locked
Conclusion of Vector spaces
THEORIE
T
1.
Notes
Inner Product Spaces
Inner product, length, and angle
THEORIE
T
1.
Inner products on real vector spaces
ÃœBUNG
Ã
2.
Inner products on real vector spaces
9
THEORIE
T
3.
Angle
ÃœBUNG
Ã
4.
Angle
6
THEORIE
T
5.
Perpendicularity
ÃœBUNG
Ã
6.
Perpendicularity
5
Orthonormal systems
THEORIE
T
1.
The notion of orthonormal system
ÃœBUNG
Ã
2.
The notion of orthonormal system
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Properties of orthonormal systems
ÃœBUNG
Ã
4.
Properties of orthonormal systems
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Constructing orthonormal bases
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Constructing orthonormal bases
Kompletten Zugriff freischalten locked
Orthogonal projections
THEORIE
T
1.
Orthogonal projection
ÃœBUNG
Ã
2.
Orthogonal projection
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Orthogonal complement
ÃœBUNG
Ã
4.
Orthogonal complement
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Gram-Schmidt in matrix form
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Gram-Schmidt in matrix form
Kompletten Zugriff freischalten locked
Complex inner product spaces
THEORIE
T
1.
Inner product on complex vector spaces
ÃœBUNG
Ã
2.
Inner product on complex vector spaces
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Orthonormal systems in complex vector spaces
ÃœBUNG
Ã
4.
Orthonormal systems in complex vector spaces
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Orthogonal complements in complex inner product spaces
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Complex orthogonal complements
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Gram-Schmidt in complex inner product spaces
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Gram-Schmidt in complex inner product spaces
Kompletten Zugriff freischalten locked
Conclusion of Inner product spaces
THEORIE
T
1.
Bessel's Inequality
THEORIE
T
2.
End of Inner product spaces
Linear maps
Linear maps
THEORIE
T
1.
The notion of linear map
ÃœBUNG
Ã
2.
The notion of linear map
10
THEORIE
T
3.
Linear maps determined by matrices
ÃœBUNG
Ã
4.
Linear maps determined by matrices
4
THEORIE
T
5.
Composition of linear maps
ÃœBUNG
Ã
6.
Composition of linear maps
7
THEORIE
T
7.
Sums and multiples of linear maps
ÃœBUNG
Ã
8.
Sums and multiples of linear maps
Kompletten Zugriff freischalten locked
THEORIE
T
9.
The inverse of a linear map
ÃœBUNG
Ã
10.
The inverse of a linear map
Kompletten Zugriff freischalten locked
THEORIE
T
11.
Kernel and image of a linear transformation
ÃœBUNG
Ã
12.
Kernel and image of a linear transformation
Kompletten Zugriff freischalten locked
THEORIE
T
13.
Recording linear maps
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
14.
Recording linear maps
Kompletten Zugriff freischalten locked
THEORIE
T
15.
Rank–nullity theorem for linear maps
ÃœBUNG
Ã
16.
Rank-nullity theorem for linear maps
Kompletten Zugriff freischalten locked
THEORIE
T
17.
Invertibility criteria for linear maps
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
18.
Invertibility criteria for linear maps
Kompletten Zugriff freischalten locked
Matrices of Linear Maps
THEORIE
T
1.
The matrix of a linear map in coordinate space
ÃœBUNG
Ã
2.
The matrix of a linear map in coordinate space
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Determining the matrix of a linear map
ÃœBUNG
Ã
4.
Determining the matrix of a linear map
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Coordinates
ÃœBUNG
Ã
6.
Coordinates
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Basis transition
ÃœBUNG
Ã
8.
Basis transition
Kompletten Zugriff freischalten locked
THEORIE
T
9.
The matrix of a linear map
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
10.
The matrix of a linear map
Kompletten Zugriff freischalten locked
THEORIE
T
11.
Coordinate transformations
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
12.
Coordinate transformations
Kompletten Zugriff freischalten locked
THEORIE
T
13.
Relationship to systems of linear equations
ÃœBUNG
Ã
14.
Relationship to systems of linear equations
Kompletten Zugriff freischalten locked
Dual vector spaces
THEORIE
T
1.
The notion of dual space
ÃœBUNG
Ã
2.
The notion of dual space
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Dual basis
ÃœBUNG
Ã
4.
Dual basis
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Dual map
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Dual map
Kompletten Zugriff freischalten locked
Conclusion of Linear maps
THEORIE
T
1.
Overview of the correspondence between matrix and linear mapping
THEORIE
T
2.
Conclusion of Linear maps
Matrix calculus
Rank and inverse of a matrix
THEORIE
T
1.
Rank and column space of a matrix
ÃœBUNG
Ã
2.
Rank and column space of a matrix
14
THEORIE
T
3.
Invertibility and rank
ÃœBUNG
Ã
4.
Invertibility and rank
2
Determinants
THEORIE
T
1.
2-dimensional determinants
ÃœBUNG
Ã
2.
2-dimensional determinants
4
THEORIE
T
3.
Permutations
ÃœBUNG
Ã
4.
Permutations
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Higher-dimensional determinants
ÃœBUNG
Ã
6.
Higher-dimensional determinants
Kompletten Zugriff freischalten locked
THEORIE
T
7.
More properties of determinants
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
More properties of determinants
Kompletten Zugriff freischalten locked
THEORIE
T
9.
Row and column expansion
ÃœBUNG
Ã
10.
Row and column expansion
Kompletten Zugriff freischalten locked
THEORIE
T
11.
Row and column reduction
ÃœBUNG
Ã
12.
Row and column reduction
Kompletten Zugriff freischalten locked
THEORIE
T
13.
Cramer's rule
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
14.
Cramer's rule
Kompletten Zugriff freischalten locked
Matrices and coordinate transformations
THEORIE
T
1.
Characteristic polynomial of a matrix
ÃœBUNG
Ã
2.
Characteristic polynomial of a matrix
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Conjugate matrices
ÃœBUNG
Ã
4.
Conjugate matrices
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Characteristic polynomial of a linear map
ÃœBUNG
Ã
6.
Characteristic polynomial of a linear map
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Matrix equivalence
ÃœBUNG
Ã
8.
Matrix equivalence
Kompletten Zugriff freischalten locked
Minimal polynomial
THEORIE
T
1.
Cayley-Hamilton
ÃœBUNG
Ã
2.
Cayley Hamilton
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Division with remainder for polynomials
ÃœBUNG
Ã
4.
Division with remainder for polynomials
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Minimal polynomial
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Minimal polynomial
Kompletten Zugriff freischalten locked
Conclusion of Matrix calculus
THEORIE
T
1.
End of Matrix Calculus
Invariant subspaces of linear maps
Eigenvalues and eigenvectors
THEORIE
T
1.
Diagonal form
ÃœBUNG
Ã
2.
Diagonal form
8
THEORIE
T
3.
Eigenspace
ÃœBUNG
Ã
4.
Eigenspace
12
THEORIE
T
5.
Determining eigenvalues and eigenvectors
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Determining eigenvalues and eigenvectors
Kompletten Zugriff freischalten locked
Diagonalizability
THEORIE
T
1.
The notion of diagonalizability
ÃœBUNG
Ã
2.
The notion of diagonalizability
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Diagonalizability and minimal polynomial
ÃœBUNG
Ã
4.
Diagonalizability and minimal polynomial
Kompletten Zugriff freischalten locked
THEORIE
T
5.
The greatest common divisor of two polynomials
ÃœBUNG
Ã
6.
The greatest common divisor of two polynomials
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THEORIE
T
7.
The Euclidean algorithm
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
The Euclidean algorithm
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Invariant subspaces
THEORIE
T
1.
The notion of invariant subspace
ÃœBUNG
Ã
2.
The notion of invariant subspace
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THEORIE
T
3.
The extended Euclidean algorithm
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
4.
The extended Euclidean algorithm
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THEORIE
T
5.
Direct sum decomposition into invariant subspaces
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ÃœBUNG
Ã
6.
Direct sum decomposition into invariant subspaces
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Generalized eigenspace
ÃœBUNG
Ã
8.
Generalized eigenspace
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THEORIE
T
9.
Jordan normal form
ÃœBUNG
Ã
10.
Jordan normal form
Kompletten Zugriff freischalten locked
THEORIE
T
11.
From real to complex vector spaces and back
ÃœBUNG
Ã
12.
From real to complex vector spaces and back
Kompletten Zugriff freischalten locked
THEORIE
T
13.
Real Jordan normal form for non-real eigenvalues
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
14.
Real Jordan normal form for non-real eigenvalues
Kompletten Zugriff freischalten locked
Matrices and coordinate transformations
THEORIE
T
1.
Characteristic polynomial of a matrix
ÃœBUNG
Ã
2.
Characteristic polynomial of a matrix
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Conjugate matrices
ÃœBUNG
Ã
4.
Conjugate matrices
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Characteristic polynomial of a linear map
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Characteristic polynomial of a linear map
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Matrix equivalence
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Matrix equivalence
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Orthogonal and symmetric maps
Orthogonal maps
THEORIE
T
1.
The notion of orthogonal map
ÃœBUNG
Ã
2.
The notion of orthogonal map
5
THEORIE
T
3.
Some properties of orthogonal maps
ÃœBUNG
Ã
4.
Some properties of orthogonal maps
6
THEORIE
T
5.
Orthogonal maps and orthonormal bases
ÃœBUNG
Ã
6.
Orthogonal maps and orthogonal bases
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THEORIE
T
7.
Orthogonal matrices
ÃœBUNG
Ã
8.
Orthogonal matrices
Kompletten Zugriff freischalten locked
THEORIE
T
9.
Orthogonal transformation matrices
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
10.
Orthogonal transformation matrices
Kompletten Zugriff freischalten locked
Classification of orthogonal maps
THEORIE
T
1.
Lowdimensional orthogonal maps
ÃœBUNG
Ã
2.
Lowdimensional orthogonal maps
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Three-dimensional orthogonal maps
ÃœBUNG
Ã
4.
Three-dimensional orthogonal maps
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Jordan normal form for orthogonal maps
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Jordan normal form for orthogonal maps
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Classification of orthogonal maps
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Classification of orthogonal maps
Kompletten Zugriff freischalten locked
Isometries
THEORIE
T
1.
The notion of isometry
ÃœBUNG
Ã
2.
The notion of isometry
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Isometries and orthonormal systems
ÃœBUNG
Ã
4.
Isometries and orthonormal systems
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Equivalence of isometries
ÃœBUNG
Ã
6.
Equivalence of isometries
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Characterisation of isometries
ÃœBUNG
Ã
8.
Characterisation of isometries
Kompletten Zugriff freischalten locked
Unitary maps
THEORIE
T
1.
The notion of unitary map
ÃœBUNG
Ã
2.
The notion of unitary map
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Diagonal form for unitary maps
ÃœBUNG
Ã
4.
Diagonal form for unitary maps
Kompletten Zugriff freischalten locked
Symmetric maps
THEORIE
T
1.
The notion of symmetric map
ÃœBUNG
Ã
2.
The notion of symmetric map
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Connection with symmetric matrices
ÃœBUNG
Ã
4.
Connection with symmetric matrices
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Properties of symmetric maps
ÃœBUNG
Ã
6.
Properties of symmetric maps
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Orthonormal bases and symmetric maps
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Orthonormal bases and symmetric maps
Kompletten Zugriff freischalten locked
Applications of symmetric maps
THEORIE
T
1.
Quadratic forms
ÃœBUNG
Ã
2.
Quadratic forms
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THEORIE
T
3.
Quadrics
ÃœBUNG
Ã
4.
Quadrics
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Least squares solutions of linear equations
ÃœBUNG
Ã
6.
Least square solutions of linear equations
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Singular value decomposition
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Singular value decomposition
Kompletten Zugriff freischalten locked
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