Ronny
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 Dec16 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). Feb8 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. Feb8 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$is nonzero or in other words the matrix has full rank. Feb7 comment On matrix norm equivalence Shouldn't that also be possible – if$\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}$unitary and get – for that the case of regular matrices – also the proof? Feb6 awarded Supporter Feb6 awarded Scholar Feb6 accepted On matrix norm equivalence Feb6 comment On matrix norm equivalence Thank you, that sounds really neat, haven't hat SVD in mind on that one. Feb6 awarded Editor Feb6 revised On matrix norm equivalence Mentioned, that$\|\cdot\|_F$is the Frobenius norm. Feb6 comment On matrix norm equivalence Oh thanks, i forgot to mention, that$\|\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. Feb6 awarded Student Feb6 asked On matrix norm equivalence