3.3 Numerical Linear Algebra

: 20 minutes

NumPy offers functions for matrix operations such as addition, multiplication, dot product, decompositions, etc. These operations also apply to higher-dimensional arrays.

Basic Operations

The dot product two vectors can be computed using numpy.dot().

Recall that * computes the element-wise product of two arrays. To perform matrix multiplication, one can either use @ or numpy.dot.

numpy.linalg

Matrix decompositions such as LU, SVD, and operations like inverse and determinant are offered through the numpy.linalg module.

Commonly used numpy.linalg functions (McKinney 2017)

Method	Description
diag	Return the diagonal (or off-diagonal) elements of a square matrix as a 1D array, or convert a 1D array into a square matrix with zeros on the off-diagonal
dot	Matrix multiplication
trace	Compute the sum of the diagonal elements
det	Compute the matrix determinant
eig	Compute the eigenvalues and eigenvectors of a square matrix
inv	Compute the inverse of a square matrix
pinv	Compute the Moore-Penrose pseudoinverse of a matrix
qr	Compute the QR decomposition
svd	Compute the singular value decomposition (SVD)
solve	Solve the linear system Ax = b for x, where A is a square matrix

McKinney, Wes. 2017. Python for Data Analysis. 2nd ed. O’Reilly Media. https://www.oreilly.com/library/view/python-for-data/9781491957653/.