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Oct
29 |
comment |
Parameterize unitary without transpose
@ Robert Bryant , indeed the proof of Prop 2 is not straightforward. We show the result over $\mathbb{C}$ and, in a second step, over $\mathbb{R}$ along the same ideas you used. That was clear for me because I knew this characterization of $\sin,\cos$ since a long time. I adopted this presentation to highlight the geometric idea behind. Yes, the Kummer's result gives the surjectivity; moreover, 1. to read Kummer's proof is much easier than to study Cartan's theory. 2. I like this "story of maths" aspect. |
Oct
29 |
comment |
Parameterize unitary without transpose
@ Sebastian SchlechtClearly , Prop. 1 and 2 can be independently proved. About a name for $V$, I don't know. In general, the authors consider elements of $V$ and not the whole set. cf also Horn and Johnson; Matrix Analysis, Section 4.6 |
Oct
29 |
revised |
Parameterize unitary without transpose
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Oct
29 |
answered | Parameterize unitary without transpose |
Oct
18 |
answered | What is the time complexity of approximated SVD |
Sep
23 |
revised |
Injectivity of a multivariate homogeneous polynomial mapping
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Sep
23 |
revised |
Injectivity of a multivariate homogeneous polynomial mapping
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Sep
23 |
answered | Injectivity of a multivariate homogeneous polynomial mapping |
Sep
8 |
awarded | Yearling |
Aug
30 |
revised |
Matrix equation
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Aug
30 |
answered | Matrix equation |
Aug
29 |
revised |
Are there some algorithms to solve the diagonal matrix $X$ to the following matrix equation?
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Aug
29 |
revised |
Are there some algorithms to solve the diagonal matrix $X$ to the following matrix equation?
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Aug
29 |
answered | Are there some algorithms to solve the diagonal matrix $X$ to the following matrix equation? |
Aug
28 |
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Can the nonlinear matrix equation $Bx=p+sgn(x)$ have an explicit solution?
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Aug
28 |
revised |
Can the nonlinear matrix equation $Bx=p+sgn(x)$ have an explicit solution?
added 112 characters in body |
Aug
28 |
answered | Can the nonlinear matrix equation $Bx=p+sgn(x)$ have an explicit solution? |
Aug
27 |
comment |
Eigenvalues of the sum of two matrices, where one is $B=\operatorname{diag}(1, 0,\dots,0)$
If $B$ is a small matrix that is similar to $diag(x,0,\cdots,0)$, then we can prove a similar result. Now, if $B=diag(x_i)$ then the result does not work; for instance, if the $x_i$ are equal to $x>0$, then the eigenvalues of $A+B$ are $\geq x$ and, consequently, are always $>0$. |
Aug
27 |
comment |
Transversality in Morse theory, linear algebra version
@ Mads R. Bisgaard , what you found out is incomprehensible. |
Aug
26 |
revised |
Eigenvalues of the sum of two matrices, where one is $B=\operatorname{diag}(1, 0,\dots,0)$
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