Explore diagonalizations, including unitary and orthogonal diagonalizations, of a square matrix.
Diagonalize a matrix:
Compute an orthogonal diagonalization of a real symmetric matrix:
Calculate a unitary diagonalization of a normal matrix:
Find the Jordan canonical form of a square matrix.
Compute a Jordan decomposition:
Decompose a matrix into the product of a lower-triangular matrix and an upper-triangular matrix.
Compute the LU decomposition of a matrix:
Decompose a matrix into the product of a unitary matrix and an upper-triangular matrix.
Compute the QR decomposition of a matrix:
Decompose a matrix into the product of a unitary matrix, a diagonal matrix (of singular values) and another unitary matrix.
Compute a singular value decomposition (SVD):
Decompose a positive definite Hermitian matrix into the product of a lower-triangular matrix and its conjugate transpose.
Find the Cholesky decomposition of a matrix:
Factor a matrix into the product of a unitary matrix, a Hessenberg matrix with zero entries below the second diagonal and the inverse of the unitary matrix.
Compute a Hessenberg decomposition:
Decompose a square matrix into the product of an upper-triangular matrix and an orthogonal or unitary matrix.
Compute a Schur decomposition: