## Linear Algebra

# Decomposition

is a lower triangular matrix

is an upper triangular matrix

is an orthgonal matrix of size

is an upper triangular matrix of size

is an

matrix

is an

matrix

is the rank of

is a nonnegative diagonal matrix

and

are unitary matrices

is the conjugate transpose of

(transpose if

contains reals only)

is a diagonal matrix formed from the eigenvalues of

The columns of

are the eigenvectors of