It is also possible to detect ill-conditioning by inspecting the matrix’s singular values directly. The ratio between the largest and the smallest singular value is the condition number:

Compute the (Moore-Penrose) pseudo-inverse of a matrix. Calculate the generalized inverse of a matrix using its singular-value decomposition (SVD) and including all large singular values.

SciPy contains functions not found in numpy.linalg, such as functions related to LU decomposition and the Schur decomposition, multiple ways of calculating the pseudoinverse, and matrix …

numpy.matrix.I # property property matrix.I # Returns the (multiplicative) inverse of invertible self. Parameters: None Returns: retmatrix object If self is non-singular, ret is such that ret * self == …

This ufunc implements the C/Python operator ~. For signed integer inputs, the bit-wise NOT of the absolute value is returned. In a two’s-complement system, this operation effectively flips all the …

A matrix is a specialized 2-D array that retains its 2-D nature through operations. It has certain special operators, such as * (matrix multiplication) and ** (matrix power).

Compute the ‘inverse’ of an N-dimensional array. The result is an inverse for a relative to the tensordot operation tensordot(a, b, ind), i. e., up to floating-point accuracy, …

numpy.matrix.transpose # method matrix.transpose(*axes) # Returns a view of the array with axes transposed. Refer to numpy.transpose for full documentation. Parameters: axesNone, …

Solve a linear matrix equation, or system of linear scalar equations. Computes the “exact” solution, x, of the well-determined, i.e., full rank, linear matrix equation ax = b.

Estimate a covariance matrix, given data and weights. Covariance indicates the level to which two variables vary together. If we examine N-dimensional samples, X = [x 1, x 2, x N] T, then the …