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Matrices as linear transformations
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Matrices act as a transformation by multiplying vectors
Matrix-vector multiplication is a linear transformation.
Definition of the standard matrix for a linear transformation
A linear transformation is given by a matrix whose columns are the images of the standard basis vectors
A linear transformation is given by a matrix with respect to a given basis.
Definition of nilpotent linear transformation
Definition of matrix representation of a linear transformation
Matrix representation of a composition of linear transformations is given by a matrix product
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A linear transformation is given by a matrix whose columns are the images of the standard basis vectors
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Matrices as linear transformations