VII. Prove the following statements. 1. Let B be an orthonormal basis of a finite-dimensional inner product space V. Suppose that the a1 02 coordinate vector [v]B = Then |v|a₁|²+|a₂|² + = ·+|an|². 2. If A is similar to a diagonal matrix D then A is similar to AT. 3. Let A be an n x n matrix with eigenvalues A₁ and A2, where A₁ A2. If Sx, is the eigenspace associated with Ai, i = 1,2, then Sx, Sx₂ = {0}.
VII. Prove the following statements. 1. Let B be an orthonormal basis of a finite-dimensional inner product space V. Suppose that the a1 02 coordinate vector [v]B = Then |v|a₁|²+|a₂|² + = ·+|an|². 2. If A is similar to a diagonal matrix D then A is similar to AT. 3. Let A be an n x n matrix with eigenvalues A₁ and A2, where A₁ A2. If Sx, is the eigenspace associated with Ai, i = 1,2, then Sx, Sx₂ = {0}.
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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