Suppose V is a finite dimensional inner product space, and dim V = n. If is...

Question

Question

Suppose V is a finite dimensional inner product space, and dim V = n.

If W = { 1, ... , Um} is an orthogonal subset of V, prove that

a. W can be extended to an orthogonal basis $\left \{ v_{1}, ... \ ,v_{m},v_{m+1},...,v_{n}\right \}$ for V.

b. $\left \{ v_{m+1},...,v_{n}\right \}$ is an orthogonal basis for $W^{^{\perp}}$

c. $dimV=dimW+dimW^{^{\perp}}$

math algebra

Answer 1

Answer #1

tch ノノ 41込丿A カン on 彳v

Answer 2

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