Visual Studio Magazine

How to Invert a Machine Learning Matrix Using C#

Inverting a matrix is one of the most common tasks in data science and machine learning. In this article I explain why inverting a matrix is very difficult and present code that you can use as-is, or ...
Visual Studio Magazine

Matrix Inverse from Scratch Using SVD Decomposition with C#

Dr. James McCaffrey of Microsoft Research presents a full-code, step-by-step tutorial on an implementation of the technique that emphasizes simplicity and ease-of-modification over robustness and ...
Nature

Generalized Inverse of a Singular Matrix

THE problem of ‘inverting’ singular matrices is by no means uncommon in statistical analysis. Rao 1 has shown in a lemma that a generalized inverse (g-inverse) always exists, although in the case of a ...
JSTOR Daily

Improved results on the Drazin inverse of a 2 × 2 block matrix in terms of Banachiewicz-Schur forms

Abstract.In this paper, we derive a representation for the Drazin inverse of a block matrix M=( A B C D ) under the assumptions 𝐴𝐴𝜋𝐵 = 0, 𝐶𝐴𝜋𝐵 ...
JSTOR Daily

On a Relationship between the Inverse of a Stationary Covariance Matrix and the Linear Interpolator

Journal of Applied Probability, Vol. 27, No. 1 (Mar., 1990), pp. 156-170 (15 pages) Let Xt be a discrete-time multivariate stationary process possessing an infinite autoregressive representation and ...