Linear Algebra: UNIT III: Inner Product Spaces
The Gram Schmidt Orthogonalization: Theorem Part 3 - Example Solved Problems
Important Example Solved Problems - Engineering Maths or Mathematics - The Gram Schmidt Orthogonalization: Theorem Part 3 - Example Solved Problems
THE GRAM
SCHMIDT ORTHOGONALIZATION
THEOREM PART 3
WORKED EXAMPLE PROBLEMS
Example 26
Let S = { (1, 0, 1), (1, 2, 1) } in C3.
Compute the orthogonal complement S┴.
Solution:
Let S = { (1, 0, i), (1, 2, 1) }
Let us assume that the set S┴ = { (a, b, c) }
(i)
By the definition of S┴ we have
(a, b, c) (1, 0, i) = 0
⇒ (a, b, c) (1, 0, 1)T
= 0
= 0
a−ci=0
……(1)
(ii) (a, b, c) (1, 2, 1) = 0
⇒ (a, b, c) (1, 2, 1)T
= 0
a+2b+c=0
………………….(2)
Solving
equations (1) & (2) we get
a = 2i, b = − (i + 1) and c = 2
S┴ = span { 2i, − (i + 1), 2 }
Linear Algebra: UNIT III: Inner Product Spaces : Tag: maths, mathematics : - The Gram Schmidt Orthogonalization: Theorem Part 3 - Example Solved Problems
Linear Algebra: UNIT III: Inner Product Spaces
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