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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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Definition of nilpotent matrix
Every nilpotent matrix is similar to a sum of nilpotent Jordan blocks
A complex square matrix is nilpotent iff all its eigenvalues are zero
Definition of index of nilpotency
Commuting diagonalizable and nilpotent decomposition over the complex numbers

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Nilpotent matrices

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Definition of nilpotent matrixClose match
Definition of index of nilpotencyClose match
A complex square matrix is nilpotent iff all its eigenvalues are zeroClose match
Definition of nilpotent linear transformationClose match
Every nilpotent matrix is similar to a sum of nilpotent Jordan blocksClose match
Definition of nullity of a matrixClose match
Equivalence theorem for nonsingular matrices: the nullity of the matrix A is 0.Close match
Commuting diagonalizable and nilpotent decomposition over the complex numbersClose match
Matrix diagonalizationClose match
InverseClose match
Nonsingular matrices and equivalencesClose match
Particular types of matricesClose match
Equivalence theorem for nonsingular matrices: the matrix A does not have 0 as an eigenvalue.Close match
Equivalence theorem for nonsingular matrices: the null space of the matrix A is {0}.Close match
Definition of 0 matrixClose match
Equivalence theorem for nonsingular matrices: the determinant of A is nonzero.Close match
Definition of nonsingular matrix: matrix is invertibleClose match
Symmetric matricesClose match
Normal matricesClose match
Definition of nonsingular matrix: the associated homogeneous linear system has only the trivial solutionClose match

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