As we've journeyed together through the realms of linear algebra, we've uncovered the powers of matrices in transforming shapes and spaces, akin to casting spells that reshape our perception of the ...

Eigenvalue problem phase 1: $\boldsymbol{A}\rightarrow \boldsymbol{H},,\left( \boldsymbol{A}\sim \boldsymbol{H} \right)$, $\boldsymbol{H}$ is a upper Hessenberg ...

Abstract: This book contains a detailed discussion of the matrix operation, its properties, and its applications in finding the solution of linear equations and determinants. Linear algebra is a ...

ABSTRACT: The paper contains two parts. First, by applying the results about the eigenvalue perturbation bounds for Hermitian block tridiagonal matrices in paper [1], we obtain a new efficient method ...

Abstract. In the present paper we are interested in the study of the distance Laplacian eigenvalues of a connected graph with fixed order n and chromatic number χ. We prove lower bounds on the ...

Here are three examples that we will consider. In each case, we have pre-computed the eigenvalues and eigenvectors (check them yourself). \[ A = \begin{bmatrix} 2 & 2 ...

In this paper, we give solvability conditions for three open problems of nonnegative inverse eigenvalues problem (NIEP) which were left hanging in the air up to seventy years. It will offer effective ...

Dear Caroline — and anyone else who has struggled with linear algebra at Tech, I read your recent article in the fifth issue of the Technique entitled “Eigenvalue issues,” in which you said that you ...