Question 14. Let -0-0-0) U2 = = 1 3√2 1 3√/2 4 1 √2 √2 3√2, (b) Let x = (1, 1, 1)T. Write x as a linear combination of u₁, U₂, and u3 using Theorem 21.13 and use Parseval's formula to compute ||x||.
Question 14. Let -0-0-0) U2 = = 1 3√2 1 3√/2 4 1 √2 √2 3√2, (b) Let x = (1, 1, 1)T. Write x as a linear combination of u₁, U₂, and u3 using Theorem 21.13 and use Parseval's formula to compute ||x||.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question

Transcribed Image Text:Question 14. Let
1
3√2
1
-@)-0-
3√2
4
3√2
=
1
3
U3 =
2
0
(b) Let x = (1, 1, 1)T. Write x as a linear combination of u₁, u2, and u3
using Theorem 21.13 and use Parseval's formula to compute ||x||.

Transcribed Image Text:Theorem 21.13 (Coordinate w.r.t orthonormal basis) Let
{u₁,,um} be the orthonormal basis for the inner product vector
space V, and for any v € V, v can be decomposed as
B
=
m
Σ < vu; > u;
i=1
Proof. For any v E V, it can be written as a linear combination of the
orthonormal basis as follows:
V = C₁U₁ +
+ Cmum
Taking the inner product with u; on both sides of the above equation, one
has:
< v, u¡ >= c; || u; ||²= c;
since u; (i = 1, ... , m) are the unit vectors.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 14 images

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

