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Engineering Mathematics
book

Engineering Mathematics

by Babu Ram
June 2009
Intermediate to advanced content levelIntermediate to advanced
1100 pages
42h 22m
English
Pearson India
Content preview from Engineering Mathematics
13.37 DIAGONALIZATION OF QUADRATIC FORMS

We know that for every real symmetric matrix A there exists an orthogonal matrix U such that

 

UT AU = diag [λ1 λ2λn],

 

where λ1, λ2,…, λn are characteristic roots of A.

Applying the orthogonal transformation X = UY to the quadratic form XTAX, we have

 

image

 

If the rank of A is r, then n-r characteristic roots are zero and so

 

image

 

where λ1, λ2,…, λn are non-zero characteristic roots.

Definition 13.112.    A square matrix B of order n over a field F is said to be congruent to another square matrix A of order ...

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Publisher Resources

ISBN: 9789332515611