1
vote
4answers
233 views

Algebra-sum of entries in each column of a sqaure matrix = constant

This is a question from an algebra homework and I am just looking for some tips. The question is: We have: $M$: an $n\times n$ matrix with real entries $c$: a real constant the ...
5
votes
1answer
206 views

eigenvalues of the sum of a matrix with known eigenvalues and a diagonal matrix

Suppose $B = A+D$, where all the eigenvalues of $A$ are already known and $D$ is a diagonal matrix, how to compute the eigenvalues of B without diagonalizing $B$ directly?
4
votes
2answers
1k views

Smallest eigenvalues of Sum of Two Positive Matrices

Let $C = A + B$, where $A$, $B$, and $C$ are positive definite matrices. In addition, $C$ is fixed. Let $\lambda (A)$, $\lambda (B)$, and $\lambda (C)$ be smallest eigenvalues of $A$, $B$, and $C$, ...