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Eine thematisch sortierte Liste von Khan-Videos zur Linearen Algebra

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Matrizen

Introduction to the matrix (HS13 Serie 2)
Matrix multiplication (part 1) (HS13 Serie 4)
Matrix multiplication (part 2) (HS13 Serie 4)
Inverse Matrix (part 1) (HS13 Serie 6)
Inverting matrices (part 2) (HS13 Serie 6)
Inverting matrices (part 3) (HS13 Serie 6)
Reduced Row Echelon Form 1 (HS13 Serie 1)
Reduced Row Echelon Form 2 (HS13 Serie 2)
Reduced Row Echelon Form 3 (HS13 Serie 3)

Kreuzprodukt (Vektorprodukt)

Cross Product Introduction (HS13 Serie 5)

Singuläre Matrizen

Singular Matrices (HS13 Serie 6)

Linearkombinationen, Span

Linear Combinations and Span (Serie 1)

Lineare Unabhängigkeit

Introduction to Linear Independence (HS13 Serie 12)
More on linear independence (HS13 Serie 12)
Span and Linear Independence Example (Serie 1)

Lineare Unterräume

Linear Subspaces (HS13 Serie 12)
Basis of a Subspace (Serie 1)

Kern und Bildraum

Introduction to the Null Space of a Matrix (Serie 5)
Null Space 2: Calculating the null space of a matrix (Serie 5)
Null Space 3: Calculating the null space of a matrix (Serie 5)
Column Space of a Matrix (Serie 5)
Null Space and Column Space Basis (Serie 5)
Dimension of the Null Space or Nullity (Serie 5)
Dimension of the Column Space or Rank (Serie 5)
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 (Serie 4)
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 (HS13 Serie 9)
nxn Determinant (HS13 Serie 10)
Determinant when row multiplied by scalar (HS13 Serie 9)
Scalar muliplication of row (HS13 Serie 9)
Determinant when row is added (HS13 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 (Serie 5)
Change of Basis Matrix (Serie 6)
Invertible Change of Basis Matrix (Serie 6)
Transformation Matrix with Respect to a Basis (Serie 6)
Alternate Basis Transformation Matrix Example (Serie 6)
Alternate Basis Transformation Matrix Example Part 2 (Serie 6)
Changing coordinate systems to help find a transformation matrix (Serie 6)

Orthogonale Basen

Introduction to Orthonormal Bases (Serie 4)
Coordinates with respect to orthonormal bases (Serie 4)
Projections onto subspaces with orthonormal bases (Serie 4)
Example using orthogonal change-of-basis matrix to find transformation matrix
Orthogonal matrices preserve angles and lengths (Serie 4)
The Gram-Schmidt Process (Serie 4)
Gram-Schmidt Process Example (Serie 4)
Gram-Schmidt example with 3 basis vectors (Serie 4)

Eigenwerte, Eigenvektoren

Introduction to Eigenvalues and Eigenvectors (Serie 2)
Example solving for the eigenvalues of a 2x2 matrix (Serie 2)
Finding Eigenvectors and Eigenspaces example (Serie 2)
Eigenvalues of a 3x3 matrix (Serie 2)
Eigenvectors and Eigenspaces for a 3x3 matrix (Serie 2)
Showing that an eigenbasis makes for good coordinate systems (Serie 7)

 

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© 2016 Mathematics Department | Imprint | Disclaimer | 27 March 2014
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