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Results tagged with linear-algebra
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user 5005
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
0
votes
Problems concerning subspaces of $M_n(\mathbb{C})$
no,it's not a homework. Do you think a homework can be so hard as these ones? :P.
I proposed them by myself. of course I don't konw whether others have solved them. They are very 'natrul' and easy to …
- 363
1
vote
2
answers
437
views
A problem concerning two symmetric matrices
Let A , B denote two symmetric matrices of the same order n. and Spec(A)=X , Spec(B)=Y.
If Spec(A+B)=X $\cup$ Y , proof thar AB=0.
here Spec(A) means the set of the engevalues of A.
This is a probl …
- 363
3
votes
What is the difference between matrix theory and linear algebra?
My opinion: matrix theory mostly deals with matrix of a paticular kind , or a few relevant ones. But linear algebra cares about the general, underlying structrue.
- 363
2
votes
0
answers
2k
views
A square matrix is congruent to its transpose
we know a square matrix is similar to its transpose, this result holds true over any field.
for they have the same "invariant factors".
Similarly, it has been proven that a square matrix is congruent …
- 363
19
votes
4
answers
2k
views
Problems concerning subspaces of $M_n(\mathbb{C})$
Let $M_n(\mathbb{C})$ denote the n times n matrices over the complex number field. N be a subspace of $M_n(\mathbb{C})$.
If all the matrices in N are non-invertible , what is the maximum the dimensi …
- 363