I don't know for sure the source of the term "singular", but one reason to call matrices singular when the determinant vanishes, is that curves and surfaces and manifolds have singularities, …

Mar 30, 2018 · A matrix A A is called left-invertible if it has a left inverse, right-invertible if it has a right inverse, and invertible if it is a square matrix that has left and right inverses. Determinant …

Oct 31, 2016 · For 1 × 1 1 × 1 matrices (i.e., numbers), the only singular matrix is 0 0; so if we add it to any nonsingular (invertible) matrix, it remains nonsingular. So to find a counterexample, …

Feb 17, 2020 · A matrix/system of equations is singular is there are infinite solutions, but iff there is a unique solution then its non-singular? I haven't learned how to take a determinant yet.

Jun 25, 2022 · In words: a matrix is invertible if I can find some matrix such that the two matrices multiplied together gives the identity (regardless of which way they're multiplied). Wherever …

I am struggling with specific matrices that are singular, but I would like to make them invertible (non-singular). My first ideas are: to eliminate certain rows and columns; to find "healthy"

Oct 11, 2018 · We show by induction that every n × n matrix A with nonsingular leading principal minors has a factorization A = LU where L is strictly lower triangular, U is upper triangular, and …

Sep 14, 2020 · If a square matrix with real entries is positive-definite, then its determinant is positive. But not conversely: Some square matrices with real entries have a positive …

Assuming that by “singular”, you mean a square matrix that is not invertible: Lemma: If A A is invertible and λ λ is an eigenvalue of A A, then 1 λ 1 λ is an eigenvalue of A−1 A − 1.

Dec 25, 2014 · Depends how far into linear algebra you are and what you can use. One possible and very short solution: a square matrix is nonsingular iff its determinant is nonzero. Now use …