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A(n×n) matrix with real elements k:=|w_max/w_min|, w- matrix singular values. Are those statements true? Why?
a) ||exp(A)||≤exp(||A||)
b) w_min(exp(A))≥exp(w_min(A))
c) k(exp(A))≤exp(k(A))
d) k(exp(A))≤exp(2*||A||)
e) Rank(exp(A))≥Rank(A)
f) Rank(exp(A))≤Rank(A)
Let M' be set of vectors orthogonal to M.
Prove or disprove: For each Hilbert subset M ⇒ M is subset of (M')'
I am sorry, I guess I wrote it not correctly:
I meant (./.) as inner product.
Looks like I should write:
Given:|(x,y)|² = (x,x)(y,y)
Prove: x and y linearly dependent
I guess I do not catch something.
Given: |(x/y)|² = (x/x)(y/y)
Prove: x and y are linearly dependent.
How do I do that?
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