138 reputation
4
bio website
location
age
visits member for 2 years, 10 months
seen Jul 1 at 17:19

Dec
16
comment Writing Complex Numbers in Standard Form
You have to be carefull, when defining the imaginary unit as you did, see en.wikipedia.org/wiki/Imaginary_unit#Proper_use - the correct way is, to say that (i) is defined by (i^2 = -1), which is note the same as your definition (to be precise, the root is not defined for complex numbers).
Feb
8
comment On matrix norm equivalence
Oh, nevermind. I think i thought of normal matrices, though i wanted to proof it for regular matrices using eigenvalues. My mistake. Thanks for the counter example and the explanations.
Feb
8
comment On matrix norm equivalence
For normal matrices, your argumentation is clear, using eigenvalues. But with regular i meant, that the determinant of §\mathbf M$ is nonzero or in other words the matrix has full rank.
Feb
7
comment On matrix norm equivalence
Shouldn't that also be possible – if $\mathbf{M}$ is regular – to take your proof and use then the unitary basis of the eigenspaces, hence choose $\mathbf{Q}$ in the diagonalizable representation $\mathbf{Q}\mathbf{\Lambda}\mathbf{Q}^{-1}$ unitary and get – for that the case of regular matrices – also the proof?
Feb
6
awarded  Supporter
Feb
6
awarded  Scholar
Feb
6
accepted On matrix norm equivalence
Feb
6
comment On matrix norm equivalence
Thank you, that sounds really neat, haven't hat SVD in mind on that one.
Feb
6
awarded  Editor
Feb
6
revised On matrix norm equivalence
Mentioned, that $\|\cdot\|_F$ is the Frobenius norm.
Feb
6
comment On matrix norm equivalence
Oh thanks, i forgot to mention, that $\|\cdot\|_F$ is (as the letter might indicate) the Frobenius norm. And yes you're right, the supremum should do. I think $B$ should be finite for the (now two) mentioned norms, but i haven't found anything.
Feb
6
awarded  Student
Feb
6
asked On matrix norm equivalence