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Examination in the School of Mathematical Sciences
Semester 1, 2015
019786 MATHS 1011
Mathematics IA
019786 MATHS 1011BR Mathematics
Mathematics IA Assignment 4
Semester 2, 2016
Algebra
In lectures we calculated the inverse of
0 1
A= 1 0
2 1
the matrix
0
1
1
by the sequence of row operations
1. R1 R2
2. R3 R3 + 2R1
3. R3 R3 R2
4. R
Mathematics IA Assignment 9
Semester 2, 2016
Algebra
Fix a value R. Consider the matrix
cos()2 sin()2
2 cos() sin()
A=
.
2 cos() sin()
sin()2 cos()2
(a) Determine the eigenvalues 1 and 2 of A.
(Hint:
Mathematics IA Assignment 6
Semester 2, 2016
Algebra
Consider the linear optimisation problem with inputs x, y and constraints
x + 2y 10
x+y 7
x6
x 1
y0
and a profit function
f (x, y) = 2x 4y.
(a) Dra
Mathematics IA Assignment 7
Semester 2, 2016
Algebra
(a) Let cfw_v1 , v2 , v3 be a set of vectors that is linearly dependent.
Show that for any other vector w, the larger set cfw_v1 , v2 , v3 , w
is
Mathematics IA Assignment 3
Semester 2, 2016
Algebra
Consider the matrix A given by
1
1
1
1 1s 1s
s 1 s s2 s
for s R.
(a) For which values of s does the inverse exist, and why? You need
to quote a re
Mathematics IA Assignment 5
Semester 2, 2016
Algebra
a b c
Let M = 0 d e be an upper triangular matrix, for a, b, c, d, e, f
0 0 f
R.
(a) Calculate adj(M ).
(b) Write down M 1 , under the assumption
Lecture for academic seminar
An Introduction to Compressed Sensing
Fang-Ming Han
[email protected]
Information Processing Laboratory, Tsinghua University
Lecture for academic seminar
Contents
I.
B
The Matrix Cookbook
[ http:/matrixcookbook.com ]
Kaare Brandt Petersen
Michael Syskind Pedersen
Version: November 14, 2008
What is this? These pages are a collection of facts (identities, approximatio
0-1
Short introduction to OFDM
Mrouane Debbah
Abstract
We provide hereafter some notions on OFDM wireless transmissions. Any comments should be sent to: Mrouane
Debbah, Alcatel-Lucent Chair on Flexibl
Student ID:
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Other names:
Desk number:
Date:
Signature:
Examination in the School of Mathematical Sciences
Semester 1, 2015
019786 MATHS 1011
Mathematics IA
019786 MATHS 1011BR Mathematics