`ulab.numpy.linalg`¶

ulab.numpy.linalg.cholesky(A: ulab.numpy.ndarray)
Parameters:

A (ndarray) – a positive definite, symmetric square matrix

Return ~ulab.numpy.ndarray L:

a square root matrix in the lower triangular form

Raises:

ValueError – If the input does not fulfill the necessary conditions

The returned matrix satisfies the equation m=LL*

ulab.numpy.linalg.det(m: ulab.numpy.ndarray)
Param:

m, a square matrix

Return float:

The determinant of the matrix

Computes the eigenvalues and eigenvectors of a square matrix

ulab.numpy.linalg.eig(m: ulab.numpy.ndarray)
Parameters:

m – a square matrix

Return tuple (eigenvectors, eigenvalues):

Computes the eigenvalues and eigenvectors of a square matrix

ulab.numpy.linalg.inv(m: ulab.numpy.ndarray)
Parameters:

m (ndarray) – a square matrix

Returns:

The inverse of the matrix, if it exists

Raises:

ValueError – if the matrix is not invertible

Computes the inverse of a square matrix

ulab.numpy.linalg.norm(x: ulab.numpy.ndarray)
Parameters:

x (ndarray) – a vector or a matrix

Computes the 2-norm of a vector or a matrix, i.e., `sqrt(sum(x*x))`, however, without the RAM overhead.

ulab.numpy.linalg.qr(m: ulab.numpy.ndarray)
Parameters:

m – a matrix

Return tuple (Q, R):

Factor the matrix a as QR, where Q is orthonormal and R is upper-triangular.