5.1. THE LINEAR CONJUGATE GRADIENT METHOD 10 set of nonzero vectors {Po, P1, ..., Pi} is said to be conjugate with respect to the symmetric positive definite matrix A if pl Ap; = 0, for all i j. (5.5) It is easy to show that any set of vectors satisfying this property is also linearly independent.

Algebra & Trigonometry with Analytic Geometry
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ISBN:9781133382119
Author:Swokowski
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Chapter3: Functions And Graphs
Section3.3: Lines
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Hi, my question is how to show that show

that any set of vectors satisfying this property (highlighted) is also linearly independent

5.1.
THE LINEAR CONJUGATE GRADIENT METHOD
set of nonzero vectors {Po, P1, ·· Pi} is said to be conjugate with respect to the symmetric
positive definite matrix A if
pl Ap; = 0, for all i ‡ j.
It is easy to show that any set of vectors satisfying this property is also linearly independent.
(5.5)
103
Transcribed Image Text:5.1. THE LINEAR CONJUGATE GRADIENT METHOD set of nonzero vectors {Po, P1, ·· Pi} is said to be conjugate with respect to the symmetric positive definite matrix A if pl Ap; = 0, for all i ‡ j. It is easy to show that any set of vectors satisfying this property is also linearly independent. (5.5) 103
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