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Results tagged with linear-algebra
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user 19077
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
0
votes
Kernel of $AB$ if $[A,B]=0$ and $AB\neq0$?
Here is an intuitive way to see why this must be false. You want to establish an equality, so your (dependent) inequalities 2) and 4) are suspect; inequalities are seldom useful in proofs of equalitie …
- 1,683
24
votes
Example for column rank $\neq$ row rank
I will only consider matrices over division rings, since defining rank over more general rings, in particular those with zero divisors, involves difficulties rather independent of those posed by non-c …
- 1,683
6
votes
Expressing $-\operatorname{adj}(A)$ as a polynomial in $A$?
This formula can be obtained during a proof of the Cayley-Hamilton theorem, as is indicated on its Wikipedia article. The essence of the argument is that Euclidean division by a monic polynomial (on t …
- 1,683