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Introduction to the matrix (HS14 Serie 2)
Matrix multiplication introduction (mehrere Videos) (HS14 Serie 4)
Inverse matrix (part 1) (HS14 Serie 6)
Inverting matrices (part 2) (HS14 Serie 6)
Inverting matrices (part 3) (HS14 Serie 6)
Reduced row echelon form 1 (HS14 Serie 1)
Reduced row echelon form 2 (HS14 Serie 2)
Reduced row echelon form 3 (HS14 Serie 3)
Cross product Introduction (HS14 Serie 5)
Singular Matrices (HS14 Serie 6)
Linear combinations and span (Serie 1)
Introduction to linear independence (HS14 Serie 12)
More on linear independence (HS14 Serie 12)
Span and linear independence example (Serie 1)
Linear subspaces (HS14 Serie 12)
Basis of a subspace (Serie 1)
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: Relation to linear independence (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
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
Exploring the solution set of Ax=b
Deriving a method for determining inverses
Example of finding matrix inverse
Formula for 2x2 inverse
3x3 determinant (HS14 Serie 9)
nxn determinant (HS14 Serie 10)
Determinant when row multiplied by scalar (HS14 Serie 9)
(correction) scalar muliplication of row (HS14 Serie 9)
Determinant when row is added (HS14 Serie 9)
Projections onto subspaces
A Projection onto a subspace is a linear transformation
Subspace projection matrix example
Projection is closest vector in subspace
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)
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)
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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