Orthonormal Study guides, Study notes & Summaries
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MAT2611 Assignment 7 2023
- Exam (elaborations) • 12 pages • 2023
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MAT2611 Assignment 7 2023 100% TRUSTED workings, explanations and solutions. For assistance call or whatsapp us on +25477 954 0132 . 
Problem 23. Show that the following identity holds for vectors in any inner 
product space. 
ku + vk 2 
+ ku vk 2 
= 2 kuk 2 
+ 2 kvk 2 
: 
[25 marks] 
Problem 24. Use inner product 
< p; q > = 
Z 1 
0 
p (x) q (x) dx 
on P3, to compute < p; q > for p = 1 x2 
, q = 2 + x 
3 
. 
[25 marks] 
Problem 25. Find all values of k for which the vector u and v a...
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Introduction to Applied Linear Algebra Vectors, Matrices, and Least Squares
- Exam (elaborations) • 473 pages • 2024
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I Vectors 1 
1 Vectors 3 
1.1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
1.2 Vector addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 
1.3 Scalar-vector multiplication . . . . . . . . . . . . . . . . . . . . . . . . 15 
1.4 Inner product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 
1.5 Complexity of vector computations . . . . . . . . . . . . . . . . . . . . 22 
Exercises . . . . . . . . . . . . . . . . . . . . . . ...
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Math 475: Partial Differential Equations
- Exam (elaborations) • 19 pages • 2023
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Math 475: Partial Differential Equations 
Shereen Elaidi 
Fall 2019 Term 
Contents 
1 Introduction 2 
1.1 Domains and Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
1.1.1 What are the main boundary conditions? . . . . . . . . . . . . . . . . . . . . . 3 
1.2 Classification of PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
2 Diffusion 4 
2.1 Derivation and Setting Up (n = 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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Lecture 11: Finding Orthonormal Bases
- Class notes • 2 pages • 2023
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- R152,71
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
5.1 Orthogonal Projections and Orthonormal Bases 
5.2 Gram-Schmidt Process and QR Factorization
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Lecture 10: Orthogonality
- Class notes • 3 pages • 2023
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Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 
5.1 Orthogonal Projections and Orthonormal Bases
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Exam (elaborations) TEST BANK FOR Digital Communications 5th Edition By Proakis Salehi (Instructor Solution Manual)
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Exam (elaborations) TEST BANK FOR Digital Communications 5th Edition By Proakis Salehi (Instructor Solution Manual) 
Solutions Manual 
for 
Digital Communications, 5th Edition 
(Chapter 2) 1 
Prepared by 
Kostas Stamatiou 
January 11, 2008 
1PROPRIETARY MATERIAL. 
c The McGraw-Hill Companies, Inc. All rights reserved. No part of this 
Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written 
permission of the publisher, or used beyond the limite...
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Orthonormal bases and orthogonal matrices
- Other • 15 pages • 2022
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Linear Algebra
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Quantum Mechanics-I Problem Set
- Other • 13 pages • 2023
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Concise collection of assignment questions on following topics in Quantum Mechanics-I. 
FAILURE OF CLASSICAL PHYSICS - blackbody radiation, atomic spectroscopy, photoelectric effect, Compton effect, de Broglie’s hypothesis, Davisson-Germer experiment, double slit experiment. 
WAVE STATE - Born interpretation and probability density, linear superposition, uncertainty principle, time-dependent and time-independent Schrodinger equation, free particle Gaussian, wavepackets and Fourier transform. 
...
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Exam (elaborations) TEST BANK FOR Principles of Communication Systems, Modulation and Noise 5th Edition By R. E. Ziemer and W. H. Tranter (SOLUTION MANUAL)
- Exam (elaborations) • 330 pages • 2021
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Exam (elaborations) TEST BANK FOR Principles of Communication Systems, Modulation and Noise 5th Edition By R. E. Ziemer and W. H. Tranter (SOLUTION MANUAL) 
Chapter 2 
Signal and Linear System Theory 
2.1 Problem Solutions 
Problem 2.1 
For the single-sided spectra, write the signal in terms of cosines: 
x(t) = 10cos(4πt + π/8) + 6 sin(8πt + 3π/4) 
= 10cos(4πt + π/8) + 6 cos(8πt + 3π/4 − π/2) 
= 10cos(4πt + π/8) + 6 cos(8πt + π/4) 
For the double-sided spectra, write the signal i...
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MAT2611 Sem ONE Assign NINE 2022
- Other • 9 pages • 2022
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MAT2611 Semester ONE Assignment NINE 2022 of solutions.
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