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: For simplicity, you can write c = cos() and s = sin(),
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) Draw the feasible region C for this optimisation problem i
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 also linearly dependent.
(b) Give a list of four distin
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 result or theorem from lectures to justify your answer.
(
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 M is invertible.
Solution:
(a) The adjoint is
d
0
Lecture for academic seminar
An Introduction to Compressed Sensing
Fang-Ming Han
fmhan@tsinghua.edu.cn
Information Processing Laboratory, Tsinghua University
Lecture for academic seminar
Contents
I.
Background
II.
Compressed Sensing
III.
Compressed Signal
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, approximations, inequalities, relations, .) about matrices and matt
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 Flexible Radio, Supelec, 3 rue Joliot-Curie 91192 GIF SUR YVET
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. R1 R1 R3
(a) Write down the sequence of the inverses E11