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Eine thematisch sortierte Liste von Khan-Videos zur Linearen Algebra

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Matrizen

Introduction to the matrix (Serie 2)
Matrix multiplication introduction (mehrere Videos) (Serie 4)
Inverse matrix (part 1) (Serie 6)
Inverting matrices (part 2) (Serie 6)
Inverting matrices (part 3) (Serie 6)
Reduced row echelon form 1 (Serie 1)
Reduced row echelon form 2 (Serie 2)
Reduced row echelon form 3 (Serie 3)

Kreuzprodukt (Vektorprodukt)

Cross product Introduction (Serie 5)

Singuläre Matrizen

Singular Matrices (Serie 6)

Linearkombinationen, Span

Linear combinations and span

Lineare Unabhängigkeit

Introduction to linear independence (Serie 12)
More on linear independence (Serie 12)
Span and linear independence example

Lineare Unterräume

Linear subspaces (Serie 12)
Basis of a subspace

Kern und Bildraum

Introduction to the null space of a matrix
Null space 2: Calculating the null space of a matrix
Null Space 3: Relation to linear independence
Column space of a matrix
Null space and column space basis
Dimension of the null space or nullity
Dimension of the column space or rank
Showing relation between basis cols and pivot cols

Lineare Abbildungen

Linear transformations
im(T): Image of a transformation
Preimage and kernel example
Linear transformation examples: Scaling and reflections
Linear transformation examples: Rotations in R2
Rotation in R3 around the x-axis
Introduction to projections
Expressing a projection on to a line as a matrix vector product
Compositions of linear transformations 1
Compositions of linear transformations 2

Lineare Gleichungen

Exploring the solution set of Ax=b
Deriving a method for determining inverses
Example of finding matrix inverse
Formula for 2x2 inverse

Determinanten

3x3 determinant (Serie 9)
nxn determinant (Serie 10)
Determinant when row multiplied by scalar (Serie 9)
(correction) scalar muliplication of row (Serie 9)
Determinant when row is added (Serie 9)

Projektionen

Projections onto subspaces
A Projection onto a subspace is a linear transformation
Subspace projection matrix example
Projection is closest vector in subspace

Koordinaten

Coordinates with respect to a basis
Change of basis matrix
Invertible change of basis matrix
Transformation matrix with respect to a basis
Alternate basis transformation matrix example
Alternate basis transformation matrix example part 2
Changing coordinate systems to help find a transformation matrix

Orthogonale Basen

Introduction to orthonormal bases
Coordinates with respect to orthonormal bases
Projections onto subspaces with orthonormal bases
Example using orthogonal change-of-basis matrix to find transformation matrix
Orthogonal matrices preserve angles and lengths
The Gram-Schmidt process
Gram-Schmidt process example
Gram-Schmidt example with 3 basis vectors

Eigenwerte, Eigenvektoren

Introduction to eigenvalues and eigenvectors
Example solving for the eigenvalues of a 2x2 matrix
Finding eigenvectors and eigenspaces example
Eigenvalues of a 3x3 matrix
Eigenvectors and eigenspaces for a 3x3 matrix
Showing that an eigenbasis makes for good coordinate systems

 

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© 2016 Mathematics Department | Imprint | Disclaimer | 19 September 2014
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