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Linear systems have 0
Linear systems of equations
Linear transformations
LU decomposition
Matrices
Matrices act as a transformation by multiplying vectors
Matrices as linear transformations
Matrix addition is commutative and associative.
Matrix adjoint is an involution.
Matrix conjugation is an involution.
Matrix describing a rotation of the plane
Matrix diagonalization
Matrix equations
Matrix equivalence
Matrix inverse is an involution.
Matrix inverses are unique: if A and B are square matrices
Matrix multiplication can be viewed as the dot product of a row vector of column vectors with a column vector of row vectors
Matrix multiplication is associative.
Matrix multiplication is distributive over matrix addition.
Matrix multiplication is not commutative in general.
Matrix representation of a composition of linear transformations is given by a matrix product
Matrix-scalar multiplication is commutative
Matrix-scalar product is commutative
Matrix transpose commutes with matrix inverse.
Matrix transpose is an involution.

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