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Linear Algebra With Applications
Found in: Page 400
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

Consider a quadratic form


where A is a symmetric nxn matrix. Let v be a unit eigenvector of A, with associated eigenvalue λ. Find q(v).


See the step by step solution

Step by Step Solution

Step 1: Given Information:


Step 2: Determining q(v⇀):

Take a look at the quadratic form:


A is a nxn symmetric matrix. Let vbe the unit eigenvector of A, with lambda as the eigenvalue. Now, use the following formula to access qv:

role="math" localid="1659615170927" qv=v.Av =v.λv =λv.v =λ1

(According to the eigen value definition)


Step 3: Determining the Result:


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