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Results tagged with linear-algebra
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user 1162
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
8
votes
3
answers
413
views
What can be said about pairs of matrices P,Q that satisfies $(P^{-1})^T \circ P = (Q^{-1})^T...
Let $P,Q$ be $n$ by $n$ invertible matrices. Suppose further that $P$ and $Q$ satisfies the following equation :
$$(P^{-1})^T \circ P = (Q^{-1})^T \circ Q$$
where $\circ$ denotes the Hadamard matrix …
- 2,154
2
votes
1
answer
807
views
On matrices that almost have the same eigenvalues
Let $A$ and $B$ be two $4\times 4$ matrices. Using Newton's identities, one can prove that if
$$\det(A) = \det(B)\quad \text{and}\quad \mathrm{tr}(A^i) = \mathrm{tr}(B^i)$$ for $i=1,2,3$, then $A$ and …
- 2,154