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Echelon matrices
Definition of unit matrix
Definition of permutation matrix
Elementary matrices
Triangular matrices
Block matrices
Symmetric matrices
Nilpotent matrices
Definition of orthogonal matrix
Unitary matrices
Definition of band matrix
Definition of Vandermonde matrix
Definition of Markov matrix
Hermitian matrices
Normal matrices
The eigenvalues of a triangular matrix are the entries on the main diagonal.
A matrix with real entries has eigenvalues occurring in conjugate pairs.
Hermitian matrices have real eigenvalues.
Distinct eigenvalues of a Hermitian matrix have orthogonal eigenvectors.
Definition of positive-definite matrix
Formula for the determinant of a 2-by-2 matrix.
Formula for the determinant of a 3-by-3 matrix.
The determinant of a triangular matrix is the product of the entries on the diagonal.
Theorem describing the determinants of elementary matrices.

Example of putting a matrix in echelon form
Example of putting a matrix in echelon form and identifying the pivot columns
Definition of (echelon matrix/matrix in (row) echelon form)
Gauss-Jordan procedure to put a matrix into reduced row echelon form
Example of (echelon matrix/matrix in (row) echelon form)
Definition of (row) echelon form of a matrix
Definition of matrix in reduced row echelon form
Definition of reduced row echelon form of a matrix
Definition of row reduce a matrix
Example of row reducing a 3-by-3 matrix
Example of row reducing a 4-by-4 matrix
Every matrix is row-equivalent to a matrix in reduced row echelon form.
Every matrix is row-equivalent to only one matrix in reduced row echelon form.
Definition of extended reduced row echelon form of a matrix
Theorem describing properties of the block matrices of the extended reduced row echelon form of a matrix
Theorem describing spaces associated to the block matrices of the extended reduced row echelon form of a matrix
Theorem describing the dimension of spaces associated to the block matrices of the extended reduced row echelon form of a matrix

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