Let $A$ and $B$ square real matrices. I know that the matrix $A+B$ has 1 as eigenvalue of multiplicity 1 and the others eigenvalues have their modulus <1. Can we say something a …

Given a matrix $M$ of size $n\times n,$ we write its different eigenvalues by $x_1,x_2,\ldots,x_m$ with $m\leq n$ such that $|x_1|>|x_2|>|x_3|>\cdots|x_m|,$ and call $x_2\doteq |\l …

I am trying to prove that a mapping has a unique fixed-point by showing that its Jacobian is a P-matrix. In this particular case the Jacobian can be decomposed as the sum of two ma …

Is there a practical way to compute the permanent of a large ($91 \times 91$) $(0,1)$ matrix? I have tried to use the matlab function written by Luke Winslow which works great for …

Background: Let $\mathcal{K}$ be set (convex cone, if you like) of symmetric matrices of order $n$. Each matrix $A \in \mathcal{K}$ can be decomposed in a unique way as $A=A_{+} …

Hello, I have two n*n correlation matrices with values ranging between -1,1. (2 correlation matrix because I have the same n terms under 2 different conditions) I then transformed …

Is the DFT matrix the unique* unitary matrix with all entries of same magnitude? (*up to some trivial transformations)

Let $A$ be an invertible matrix with positive eigenvalues and $B$ be a positive definite matrix . How to estimate the minimum eigenvalues of $AB$ by using the eigenvalues of $A$ an …

What can one say about a matrix for which the inverse of each leading principal minor is equal to the leading principal minor of its inverse (of the same dimensions, of course)? Fo …

Let $A$ be a real symmetric $n\times n$ matrix normalised such that $Tr[A]=1$. Define 'fischer basis' as the basis in which all diagonal elements are equal to $\frac{1}{n}$. The m …

If N>2, it is well known that if two invertible NxN matrices A and B have the same determinants of any 2x2 corresponding submatrices, then A=B or A=-B. Given then all these 2x2 det …

Let $M$ be a $2^n \times 2^n$ matrix over real number field, where the rows and columns are indexed by subsets of $[n] := {1,2,\ldots,n}$, and defined as follows, $ M_{A, B} = 1 $ …

Hello, In my work in PDE, the following problem in linear algebra came up. Any help in this direction is appreciated. QUESTION: Let $m,n\in\mathbb{N}$ and let $A_1,\ldots, A_m …

Edit: Maybe I should make it clear that by a solution I mean a pair of matrices $(A,B)$ such that the identity below holds for any complex numbers $x,y$. One of my friend asked me …

I have a $n \times n$ real-valued symmetric matrix $A$ with only zeros and ones as its entries ($A$ can be thought of as the adjacency matrix of a graph), such that the diagonal en …