1
vote
0answers
56 views

A Unique Invariant subspace for a set of matrices

Im wondering if anyone can give me a good reference or answer this question which may have already be solved. For a set of generic $n\times n$ matrices $A_1,A_2,...,A_k$, such that they share only ...
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1answer
127 views

endomorphism and subspace

Let $\phi: V \to V$ be an endomorphism over a $\mathbb{C}$-field. Show: If there is a decomposition $V = V_1 \oplus V_2$ with $V_1,V_2 \neq \{0\}$ and $\phi$-invariant, then there exist ...
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1answer
1k views

Invariants of a matrix

I'm teaching a course in physics, and I need a simple and intuitive proof that a matrix ($3\times3$, but it doesn't matter) has exactly 1 invariant which is linear in its entries, 2 that are ...