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Results tagged with linear-algebra
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user 6827
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
29
votes
Accepted
When is $\ker AB = \ker A + \ker B$?
Since $\ker A = \ker A^2$, the map $\bar{A} : V/\ker A \to V/\ker A$ is injective. Since $V/\ker A$ is finite dimensional, this map is surjective. So for any $x \in V$ we can find $y \in V$ and $z \in …
- 3,702
7
votes
Accepted
ad (A^n) is a polynomial in ad A ?
I don't think it's true even when $A$ is diagonalisable.
Suppose that $A$ is a diagonal matrix, with $(i,i)$th entry $\lambda_i$; thus $A = \rm{diag}$$(\lambda_i)$. Then we can write $\rm{ad}(A) = \r …
- 3,702