Canonical form derivation of (L1'AL1)

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SUMMARY

The discussion centers on the derivation of the canonical form of the expression L'AL1, specifically addressing the equation γΛγ1 = Σy2λ = 1. The participant clarifies that this equation is not arbitrary but results from the derivation process involving the symmetric matrix Δ = L'1AL1. The matrix L is defined as a 1x3 matrix of eigenvalues of the symmetric matrix A, and the expression y'Δy represents the multiplication of the transpose of vector components of y with the symmetric matrix Δ, followed by multiplication with the y vector.

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Students and professionals in mathematics, particularly those focusing on linear algebra, eigenvalue problems, and canonical forms. This discussion is also beneficial for researchers dealing with symmetric matrices in various applications.

Sanchayan Ghosh
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Hello everyone,

I actually had a problem with understanding the part where they have defined L'AL = Λ. There, they have taken
γΛγ1 = Σy2λ = 1. Why have they taken that? Is it arbitary or does it come as a result of a derivation?
Screenshot_2018-09-15-15-16-14-1646668577.png

Thank you
 

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sorry, we cannot see the picture
 
I don't know why it got blurred. Actually I resolved the problem.
y'Δy is nothing but mitiplying the transpose of vector components of y with the symmetric matrix
Δ = L'1AL1
L is the 1x3 matrix of eigen values of a symmetric matrix A.
And then multiplying the result with y vector. This gives the above expression as I had asked.

Thank you.
 

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