Versine - Wikipedia, the free encyclopedia
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Versine
From Wikipedia, the free encyclopedia
The versine or versed sine, versin(), is a trigonometric function equal to 1 cos() and 2sin2(). It
Starting with Two Matrices
Gilbert Strang, Massachusetts Institute of Technology
Imagine that you have never seen matrices. On the principle that examples are amazingly powerful, we
study two matrices
Orthogonality Tutorial
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ORTHOGONALITY TUTORIAL
TUTORIALS
TUTORIALS HOME
GENERAL MATH
NOTATION &
METHODS OF
PROOF
INDUCTION
COMPLEX
NUMBERS
POLYNOMIALS
Orthogonal Sets
Vectors v, u are ortho
LECTURE 2
Orthogonal Vectors and
Matrices
OBJECTIVE: Orthogonality is central to many of
the main algorithms on linear algebra. We review the
ingredients: orthogonal vectors and matrices.
2-1
Transp o
Chapter 04.02
Vectors
After reading this chapter, you should be able to:
1.
2.
3.
4.
5.
define a vector,
add and subtract vectors,
find linear combinations of vectors and their relationship to a set o
EE 505 B Fall 2011
Midterm Exam Solutions
1. [23 points]
(a) [3 points] b is in the column space of the matrix, or (equivalently) b is a
linear combination of the columns of A
(b) (i) [6 points] The e
EE 505 B Fall 2011
Midterm Exam
Nota bene: For full credit you must show all of the steps or reasoning that you used to
get the answer.
1. [23 points]
(a) [3 points] If one appends a column vector b t
Edward Neuman Department of Mathematics Southern Illinois University at Carbondale [email protected]
One of the nice features of MATLAB is its ease of computations with vectors and matrices. In this
Mathematics of the DFT
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Mathematics of the DFT
In the signal processing literature, it is common to write the DFT a
List of trigonometric identities - Wikipedia, the free encyclopedia
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List of trigonometric identities
From Wikipedia, the free encyclopedia
In mathematics, trigonometric identities are
equ
List of integrals of trigonometric functions - Wikipedia, the free encyclopedia
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List of integrals of trigonometric functions
From Wikipedia, the free encyclopedia
The following is a list
The Eigenvalue Problems - 8.8
1. Definition of Eigenvalues and Eigenvectors:
Let A be an n ! n matrix. A scalar ! is said to be an eigenvalue of A if the linear system Av " !v has a
nonzero solution v
EE 505 B Fall 2011
Final Exam Solutions
1. [35 points]
(a) [10 points] We use the formula
f X (x) =
f U (u)
d
du g(u) u = u i
i
x
There is only one solution u1 that sat1
ises the equation x = ln(u):
x
EE 505 B Fall 2011
Final Exam
Nota bene: For full credit you must show all of the steps or reasoning that you used to
get the answer.
1. [35 points] U is a uniformly distributed random variable with p
453.701 Linear Systems, S.M. Tan, The University of Auckland
9-1
Chapter 9 The Discrete Fourier transform
9.1
Denition
When computing spectra on a computer it is not possible to carry out the integral
Euler's Identity
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Euler's Identity
Euler's identity (or `theorem' or `formula') is
(Euler's Identity)
To `prove' th
EIGENVALUES AND EIGENVECTORS
1. Definition
They are dened in terms of each other. Let A be an n n matrix. A vector
v = 0 is an eigenvector of A with eigenvalue if the equation
Av = v
is satised.
Note
EE 500 PMP Colloquium/Seminar - UWEE - EE 500
Academics
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Academics > Course Info > Class Home Pages
Undergraduate
Master's & Ph.D.
Professional Programs
EE 500F
PMP Colloquium/Seminar
Non-D
Section 17.9 The Divergence Theorem
Turning a Flux Integral into a Triple Integral The last result we consider is a generalization of Greens Theorem converting a ux integral over a closed surface into
Divergence Theorem Examples
Gauss' divergence theorem relates triple integrals and surface integrals.
GAUSS' DIVERGENCE THEOREM Let F be a vector field. Let W be a closed surface, and let e be the reg
DFT Definition
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DFT Definition
The Discrete Fourier Transform (DFT) of a signal
where `
may be defined by
' means `
Delta Function - from Wolfram MathWorld
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Algebra
Applied Mathematics
Calculus and Analysis
Discrete Mathematics
Foundations of Mat
1.4 The Matrix Equation Ax b
Linear combinations can be viewed as a matrix-vector
multiplication.
Definition
If A is an m n matrix, with columns a 1 , a 2 , , a n , and if x is in
R n , then the produ
EE 505 B Fall 2011
Assignment 8 Solutions
For full credit, you must show all of the steps or reasoning that you used to get the
answer.
1. (a) The denition of the region can be written as
B = cfw_( x1
EE 505 B Fall 2011
Assignment 8
For full credit, you must show all of the steps or reasoning that you used to get the
answer.
1. A joint probability density function is given as
c e x1
x1 > 0 and | x2
EE 505 B Fall 2011
Assignment 7 Solutions
1. (a)
Ecfw_ X =
=
x f X ( x ) dx
b
a
x
dx
ba
b
=
=
=
=
x2
1
ba 2 a
1
( b2 a2 )
2( b a )
(b a)(b + a)
2( b a )
b+2
2
(b) We use the direct method to nd the p
EE 505 B Fall 2011
Assignment 7
For full credit, you must show all of the steps or reasoning that you used to get the
answer.
1. Let X be a random variable with a uniform probability density function.
EE 505 C, Autumn, 2010
Vector Calculus
1
1 Calculus Review
1.1 Integration over a plane (double integrals)
Integration over a plane is a special case of integrating over a surface, in which the
surfac