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Eine thematisch sortierte Liste von Khan-Videos zur Linearen Algebra
Check in the VVZ for a current information.
Matrizen
Introduction to matrices
Matrix multiplication (part 1)
Matrix multiplication (part 2)
Inverse Matrix (part 1)
Inverting matrices (part 2)
Inverting matrices (part 3)
Reduced Row Echelon Form 1
Reduced Row Echelon Form 2
Reduced Row Echelon Form 3
Singuläre Matrizen
Linearkombinationen, Span
Lineare Unabhängigkeit
Linear Algebra: Introduction to Linear Independence
More on linear independence
Span and Linear Independence Example
Lineare Unterräume
Linear Subspaces
Linear Algebra: 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: Calculating the null space of a matrix
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
Linear Algebra: Exploring the solution set of Ax=b
Linear Algebra: Deriving a method for determining inverses
Linear Algebra: Example of Finding Matrix Inverse
Linear Algebra: Formula for 2x2 inverse
Determinanten
3x3 Determinant
nxn Determinant
Determinant when row multiplied by scalar
Scalar muliplication of row
Determinant when row is added
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
Linear Algebra: 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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