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Omni-MATH / Let n be a positive integer. Find all n×n real matrices A with only real eigenvalues satisfying A+A^(k)=A^(T) for some integer k≥n.

Problem

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problem

Let nn be a positive integer. Find all n×nn \times n real matrices AA with only real eigenvalues satisfying A+Ak=ATA+A^{k}=A^{T} for some integer k≥nk \geq n.
Plain-text mathematical notation (without MathML)
Let n be a positive integer. Find all n×n real matrices A with only real eigenvalues satisfying A+A^(k)=A^(T) for some integer k≥n.
Original LaTeX notation
Let $n$ be a positive integer. Find all $n \times n$ real matrices $A$ with only real eigenvalues satisfying $$A+A^{k}=A^{T}$$ for some integer $k \geq n$.

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Source and history

task_id
9341e216-d0dd-5182-8423-bd58d8e0c437
task_key
test--9341e216-d0dd-5182-8423-bd58d8e0c437
task_revision_id
1
config / split
/ test

Official source

initial import