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Particular types of matrices

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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
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.
The eigenvalues of a triangular matrix are the entries on the main diagonal.
Theorem describing the determinants of elementary matrices.

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The determinant of a triangular matrix is the product of the entries on the diagonal.

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The eigenvalues of a triangular matrix are the entries on the main diagonal.Close match
The determinant of a block diagonal matrix is the product of the determinants of the blocks.Close match
Definition of an upper triangular matrixClose match
Triangular matricesClose match
The determinant of a matrix can be expressed as a product of the diagonal entries in a non-scaled echelon form.Close match
Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.Close match
The product of upper/lower triangular matrices is upper/lower triangular.Close match
Definition of determinant of a matrix as a cofactor expansion across the first rowClose match
Theorem describing the determinants of elementary matrices.Close match
The determinant of a matrix can be computed as a cofactor expansion across any row.Close match
The determinant of the matrix of a linear transformation is the factor by which the area/volume changes.Close match
A matrix and its transpose have the same determinant.Close match
The inverse of an invertible upper/lower triangular matrix is upper/lower triangular.Close match
The determinant of a matrix measures the area/volume of the parallelogram/parallelipiped determined by its columns.Close match
Definition of a lower triangular matrixClose match
The determinant of a matrix can be computed as a cofactor expansion down any column.Close match
Determinants and operations on matricesClose match
Determinants axiomaticallyClose match
DeterminantsClose match
Every complex square matrix is unitarily similar to an upper triangular matrixClose match

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