EECS 551: HW 3
Reading for next week: Chapter 2 and Chapter 3 of Laub
Question 1. This what is known about the dietary habits of the mythical Michigan Wolverine who eats
only grapes, cheese or lettuce
EECS 453/551: HW1 SOLUTIONS
Problem 1 (*)
m
Let e R be a vector with ei = 1 for i = 1, . . . , m. Let x Rn be a vector with xj = j for j = 1, . . . , n.
Then the desired n m matrix whose j-th row equa
EECS 551- HW 2
Reading pertaining to problem set: Chapter 2, Chapter 5.1, Chapter 9.1, Chapter 13.1-13.2
Reading for next week: Chapter 3, Chapter 5.2
Problem 1. How are eigenvalues and eigenvectors o
EECS551: HW1 SOLUTIONS
Problem 1
m
Let e R be a vector with ei = 1 for i = 1, . . . , m. Let x Rn be a vector with xj = j for j = 1, . . . , n.
Then the desired n m matrix whose j-th row equals j is g
EECS 551 - HOMEWORK 1
Reading pertaining to the problem set: Chapter 1 of Laub
Reading for next week: Chapter 2 Section 9.1 of Laub
Problem 1. Express the n m matrix A whose j th row equals j as an ou
EECS551: HW2 SOLUTIONS
Problem 1
T
Let A = QQ be the eigendecomposition of A. Then we may write
B = A 10I
= QQT 10QQT
(I = QQT since Q is orthogonal)
= Q( 10I)QT
(0.1)
Notice that 10I is a diagonal ma
EECS 551: HW 4 SOLUTIONS
Problem 1
Given A = xxT + yy T .
The rank of A is at most two. It is equal to zero when xxT = yy T and equals one when x is collinear with
y. We now treat the setting where th
EECS551: HW3 SOLUTIONS
Problem 1
The transition probability matrix is
Cheese
0
1/2
1/2
Cheese
P =
Grapes
Lettuce
Grapes
4/10
1/10
5/10
Lettuce
6/10
4/10
0
T
Let = 1 2 3 be the equilibrium distribu
EECS 551: HW 4
Question 1. What are the eigenvalues and eigenvectors of A = xxT + yy T ?
Assume that xT y = = 0
Hint: The desired eigenvectors of A must be in the range of A. Hence they must be line
EECS 551: HW 5 SOLUTIONS
Problem 1
n
T
The idea is to view the image as a matrix A = i=1 i ui vi where in this case n = 480. We know that
k
T
the optimal (with respect to any unitarily invariant norm)
EECS 551: Homework 5
Problem 0 (2 pts):
Please fill out the online course evaluation for 551. Once you complete your rating for the course, a
confirmation notice will appear on the web page. Please pr
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November 27, 2017, 09:50
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EECS 551: MATRIX METHODS FOR SIGNAL PROCESSING, DATA ANALYSIS & MACHINE LEARNING
EECS 453: APPLIED MATRIX ALGORITHMS FOR SIGNAL PROCESSING, DATA ANALYSIS & MACHINE LEARNING
Summary: Theory and applica
100
Lecture 24-25
Applications of eigen vectors and eigen values:
1. Karhunen-Loeve Transform (KLT): In many image processing applications, one
would like to transmit images (512 x 512) over a noisy c
92
Lecture 22-23
The concept of eigen values and eigen vectors is applicable to any Hilbert space and for
any linear transformation. The topic that deals with this concept is called linear operator
th
86
Lecture 21
Eigen Values and Eigen Vectors: To study linear systems we will develop the
notion of eigen functions. This notion was used in rst part of the course to introduce
Fourier transforms. Let
79
Lecture 19-20
3. Least Squares Filtering: Consider the example of acoustic echo cancellation in teleconferencing applications. Input speech signal f [n] enters the system. It is converted
into an a
67
Lecture 16-18
In many practical applications, we are asked to approximate a given signal using a linear
combination of a xed collection of elementary signals. Recall that while studying DT signals,
University of Michigan
Fall 2016
EECS 551: Midterm Exam 2
Monday November 21, 2016
Instructions:
Total points for credit = 100.
You will be provided with answer sheets separate from this question pa
Do not write in upper left corner!
October 29, 2017, 13:42
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Last (family) name:
First (given) name:
I have neither given nor received aid on this examination, nor concealed any violation of the
Last (family) name:
Do not write in upper left corner!
December 18, 2017, 21:34
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First (given) name:
I have neither given nor received aid on this examination, nor concealed any violation of the
University of Michigan
Fall 2016
EECS 551: Midterm Exam 2
Monday November 21, 2016
Instructions:
Total points for credit = 100.
You will be provided with answer sheets separate from this question pa
Do not write in upper left corner!
October 23, 2017, 09:55
Page 1
Last (family) name:
First (given) name:
I have neither given nor received aid on this examination, nor concealed any violation of the