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Vector Spaces
(m10767)
Authors:
Michael Haag
,
Steven J. Cox
,
Justin Romberg
Keywords:
complex vector spaces
,
linear function spaces
,
real vector spaces
,
vector
,
vector space
,
vector spaces
Summary:
This module will define what a vector space is and provide useful examples to the reader.
Subject:
Mathematics and Statistics
Language:
English
Popularity:
88.13%
Revised:
2010-07-29
Revisions:
7
Rating:
Not yet rated
Uniform Convergence of Function Sequences
(m10895)
Authors:
Michael Haag
,
Richard Baraniuk
Keywords:
converge
,
convergence
,
converges
,
function sequences
,
sequences
,
uniform
,
uniform convergence
Summary:
Another form of convergence, uniform convergence, is defined and described in this module. Also, its relationship to pointwise convergence is also shown.
Subject:
Mathematics and Statistics
Language:
English
Popularity:
93.81%
Revised:
2010-07-29
Revisions:
8
Rating:
Not yet rated
Types of Bases
(m10772)
Authors:
Michael Haag
,
Justin Romberg
Keywords:
basis
,
delta function
,
fourier series
,
hilbert space
,
kronecker
,
normalized
,
normalized basis
,
orthogonal
,
orthogonal basis
,
orthonormal
,
orthonormal basis
,
vector space
,
vector spaces
Summary:
This module discusses the different types of basis that leads up to the definition of an orthonormal basis. Examples are given and the useful of the orthonormal basis is discussed.
Subject:
Mathematics and Statistics
Language:
English
Popularity:
79.66%
Revised:
2010-07-29
Revisions:
8
Rating:
Not yet rated
The Z Transform: Definition
(m10549)
Author:
Benjamin Fite
Keywords:
Fourier transform
,
ROC
,
z-transform
Summary:
A brief definition of the z-transform, explaining its relationship with the Fourier transform and its region of convergence, ROC.
Subject:
Mathematics and Statistics
Language:
English
Popularity:
99.05%
Revised:
2010-07-29
Revisions:
11
Rating:
Not yet rated
Symmetry Properties of the Fourier Series
(m10838)
Author:
Justin Romberg
Keywords:
even signal
,
fourier
,
fourier series
,
odd signal
,
properties
,
symmetry
,
symmetry properties
,
symmetry property
Summary:
This module looks at the different symmetry properties of the fourier series and its fourier coefficients.
Subject:
Mathematics and Statistics
Language:
English
Popularity:
88.03%
Revised:
2010-07-29
Revisions:
6
Rating:
Not yet rated
Plancharel and Parseval's Theorems
(m10769)
Author:
Justin Romberg
Keywords:
Parseval
,
Plancharel
Summary:
This module contains the definition of the Plancharel theorem and Parseval's theorem along with proofs and examples.
Subject:
Mathematics and Statistics
Language:
English
Popularity:
89.59%
Revised:
2010-07-29
Revisions:
8
Rating:
Not yet rated
Norms
(m10768)
Authors:
Michael Haag
,
Justin Romberg
Keywords:
Euclidean norm
,
norm
,
normalization
,
normed linear space
,
normed vector space
,
norms
Summary:
This module will define a norm and give examples and properties of it.
Subject:
Mathematics and Statistics
Language:
English
Popularity:
82.19%
Revised:
2010-07-29
Revisions:
7
Rating:
Not yet rated
Orthonormal Basis Expansions
(m10760)
Authors:
Michael Haag
,
Justin Romberg
Keywords:
basis
,
basis matrix
,
coefficient vector
,
decompose
,
hilbert
,
hilbert spaces
,
orthonormal
,
orthonormal basis
,
standard basis
Summary:
The module looks at decomposing signals through orthonormal basis expansion to provide an alternative representation. The module presents many examples of solving these problems and looks at them in several spaces and dimensions.
Subject:
Mathematics and Statistics
Language:
English
Popularity:
89.86%
Revised:
2010-07-29
Revisions:
7
Rating:
Not yet rated
Matrix Equation for the DTFS
(m10771)
Author:
Roy Ha
Keywords:
basis
,
discrete-time
,
discrete time fourier series
,
dtfs
,
fourier
,
fourier series
,
matrix equation
,
standard basis
Summary:
This module looks at writing our DTFS equations in matrix form to make calculations and displaying the basis easier.
Subject:
Mathematics and Statistics
Language:
English
Popularity:
73.31%
Revised:
2010-07-29
Revisions:
8
Rating:
Not yet rated
Common Hilbert Spaces
(m10759)
Authors:
Roy Ha
,
Justin Romberg
Keywords:
hilbert
,
hilbert space
,
hilbert spaces
,
normed space
,
vector space
,
vector spaces
Summary:
This module will give an overview of the most common Hilbert spaces and their basic properties.
Subject:
Mathematics and Statistics
Language:
English
Popularity:
77.13%
Revised:
2010-07-29
Revisions:
8
Rating:
Not yet rated
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