(Difficulty: *) Consider an orthogonal basis {0:};=0..N-1 for RN. Select the statements that hold for any vector x E RN N-1 ||x|| = (x, p:)|² if and only if ||o:||2 = 1 Vi. %3D i=0 N-1 i=0 N-1 1 || |} i=0 if and only if ||oi||2 = P vi. N-1 1 ||x||} = (x, p:) |² if and only if ||Þ:|} = P vi. P i=0 ||

(Difficulty: *) Consider an orthogonal basis {0:};=0..N-1 for RN. Select the statements that hold for any vector x E RN N-1 ||x|| = (x, p:)|² if and only if ||o:||2 = 1 Vi. %3D i=0 N-1 i=0 N-1 1 || |} i=0 if and only if ||oi||2 = P vi. N-1 1 ||x||} = (x, p:) |² if and only if ||Þ:|} = P vi. P i=0 ||

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(Difficulty: *) Consider an orthogonal basis {0:};=0..N-1 for RN. Select the statements that hold for any vector x E RN
N-1
||x|| = (x, p:)|² if and only if ||0:||2 = 1 Vi.
%3D
i=0
N-1
i=0
N-1
1
|| |}
i=0
if and only if ||oi||2 = P vi.
N-1
1
||x||} = (x, p:) |² if and only if ||Þ:|} = P vi.
P
i=0
||

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