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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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Hermitian matrices have real eigenvalues.

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Hermitian matricesClose match
A matrix with real entries has eigenvalues occurring in conjugate pairs.Close match
Distinct eigenvalues of a Hermitian matrix have orthogonal eigenvectors.Close match
Every matrix has an eigenvalue over the complex numbers.Close match
Multiplication by a Hermitian matrix commutes with the standard inner product on C^n.Close match
Definition of Hermitian/self-adjoint matrixClose match
Eigenvectors of a symmetric matrix with different eigenvalues are orthogonal.Close match
Symmetric matricesClose match
Normal matricesClose match
The eigenvalues of a power of a matrix are the power the eigenvalues.Close match
Particular types of matricesClose match
Definition of positive-definite matrixClose match
Eigenvalues and operations on matricesClose match
Unitary matrices are invertible.Close match
Equivalence theorem for nonsingular matrices: the matrix A does not have 0 as an eigenvalue.Close match
A matrix and its transpose have the same eigenvalues/characteristic polynomial.Close match
Unitary matricesClose match
A matrix is orthogonally diagonalizable if and only if it is symmetric.Close match
Equivalence theorem for nonsingular matrices: the determinant of A is nonzero.Close match
Definition of eigenvalue of a matrixClose match

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