# `ulab.numpy.linalg`¶

`ulab.numpy.linalg.``cholesky`(A: ulab.numpy.ndarray)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)float
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)Tuple[ulab.numpy.ndarray, 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)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)float
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)Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]
Parameters

m – a matrix

Return tuple (Q, R)

Computes the QR decomposition of a matrix