uppose is the quadratic form Q = x Ax, where A is the symmetric matrix A = 2 he quadratic form is positive definite when c> he quadratic form is positive semi-definite when c> he quadratic form Qis indefinite when |c| < he quadratic form is negative semi-definite when c < he quadratic form Q is negative semi-definite when c< II N c) and x = X2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Suppose is the quadratic form Q = x¹ Ax, where A is the symmetric matrix A =
The quadratic form is positive definite when c >
The quadratic form is positive semi-definite when c
The quadratic form is indefinite when |c| <
The quadratic form is negative semi-definite when c <
- (22) and
The quadratic form Qis negative semi-definite when c<
and x =
(21).
Transcribed Image Text:Suppose is the quadratic form Q = x¹ Ax, where A is the symmetric matrix A = The quadratic form is positive definite when c > The quadratic form is positive semi-definite when c The quadratic form is indefinite when |c| < The quadratic form is negative semi-definite when c < - (22) and The quadratic form Qis negative semi-definite when c< and x = (21).
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