Velamma Episode 25 In Hindi Pdf
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Velamma Episode 25 In Hindi Pdf. It’s the first kuch kuch hota hindi episode, named ‘katha’s’ in hindi! Velamma may be one of the best kalpakke and even the first kalpakke film ever made in urdu.Q:
Finite Dimensional Contraction Co-Diagonalization Theorem
I’ve just read the book by Stephen C. Benton. The finite Dimensional Contraction Co-Diagonalization Theorem is:
Let $X$ be a complex inner product space and $T$ be a contractive map on $X$. We say that $T$ is co-diagonalizable if there exists a sequence $(T_n)$ of normal operators each defined on a finite dimensional space $E_n$ such that
$$T=\bigoplus T_n;$$
where the direct sum is taken over all $n$, and if $T_n$ is defined on $E_n$
then $T_n$ is normal, and is co-diagonalizable if and only if
$$T_n=T_n^{\ast}T_n.$$
He gives three applications of the theorem: linear systems (basis), matrix polynomials (minimal polynomials), and finite division (minimal polynomials again).
I’m curious as to what he has to say about those applications.
If $T_n=T_n^{\ast}T_n$, i.e. $T_n$ is normal, then the theorem states that $T_n$ is co-diagonalizable, and even if we have a basis (or something like that) to construct the normals, I’m not sure how to make use of this information.
To highlight what I’m confused about, I’ll give a specific example: for $T_n$, I could take the diagonal matrix where the diagonal entries are the eigenvalues of the normal $T_n$.
I believe this is what we need for the linear system applications, but I don’t know how to make use of this in the linear algebra applications
.
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