Sunday, June 2, 2019

linear algebra - Find the eigenvalues of a matrix with ones in the diagonal, and all the other elements equal

Let $A$ be a real $n\times n$ matrix, with ones in the diagonal, and all of the other elements equal to $r$ with $0

How can I prove that the eigenvalues of $A$ are $1+(n-1)r$ and $1-r$,
with multiplicity $n-1$?

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analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...