Skip to main content
Thammasat University Digital Collections
Home
Browse All
Log in

Help

English
English
Deutsch
Español
Pirate English
한국어 Korean
Français
ไทย Thai
Search
Advanced Search
Find results with:
error div
Add another field
Search by date
Search by date:
from
after
before
on
from:
to
to:
Searching collections:
Ebook Collection
Add or remove collections
Home
Ebook Collection
An introduction to semitensor product of matrices and ITS applications
Reference URL
Share
Add tags
Comment
Rate
To link to this object, paste this link in email, IM or document
To embed this object, paste this HTML in website
An introduction to semitensor product of matrices and ITS applications
Download
small (250x250 max)
medium (500x500 max)
Large
Extra Large
large ( > 500x500)
Full Resolution
Print
There is no file associated with this item.
Description
Rating
Title
An
introduction
to
semitensor
product
of
matrices
and ITS
applications
Creator
Cheng, DaiZhan.
Contributors
Qi, Hongsheng, Ph.D.
Zhao, Yin.
World Scientific (Firm)
DescriptionAbstract
A
generalization
of
Conventional
Matrix
Product
(CMP)
,
called
the
SemiTensor
Product
(STP)
,
is
proposed
.
It
extends
the
CMP
to
two
arbitrary
matrices
and
maintains
all
fundamental
properties
of
CMP
. In
addition
,
it
has a
pseudocommutative
property
,
which
makes
it
more
superior
to
CMP
. The
STP
was
proposed
by the
authors
to
deal
with
higherdimensional
data
as
well
as
multilinear
mappings
.
After
over
a
decade
of
development
,
STP
has been
proven
to be a
powerful
tool
in
dealing
with
nonlinear
and
logical
calculations
. This
book
is
a
comprehensive
introduction
to the
theory
of
STP
and its
various
applications
,
including
logical
function
,
fuzzy
control
,
Boolean
networks
,
analysis
and
control
of
nonlinear
systems
,
amongst
others
.
DescriptionTable Of Contents
1
.
Multidimensional
data
.
1
.
Multidimensional
data
.
1.2
.
Arrangement
of
data
.
1.3
.
Matrix
products
.
1.4
.
Tensor
.
1.5
.
Nash
equilibrium
.
1.6
.
Symmetric
group
.
1.7
.
Swap
matrix

2
.
Semitensor
product
of
matrices
.
2.1
.
Multilinear
function
.
2.2
.
Left
semitensor
product
of
matrices
.
2.3
.
Fundamental
properties
.
2.4
.
Pseudocommutativity
via
swap
matrix
.
2.5
.
Semitensor
product
as
bilinear
mapping

3
.
Multilinear
Mappings
among
vector
spaces
.
3.1
.
Cross
product
on
[symbol]
.
3.2
.
General
linear
algebra
.
3.3
.
Mappings
over
matrices
.
3.4
.
Converting
matrix
expressions
.
3.5
.
Two
applications

4
.
Right
and
general
semitensor
products
.
4.1
.
Right
STP
.
4.2
.
Semitensor
product
of
arbitrary
matrices

5
.
Rank
,
pseudoinverse
, and
positivity
of
STP
.
5.1
.
Rank
of
products
.
5.2
.
Pseudoinverse
of
STP
.
5.3
.
Positivity
of
products

6
.
Matrix
expression
of
logic
.
6.1
.
Logic
and its
expression
.
6.2
.
General
structure
of
logical
operators
.
6.3
.
Fundamental
properties
of
logical
operators
.
6.4
.
Logical
system
and
logical
inference
.
6.5
.
Multivalued
logic

7
.
Mixvalued
logic
.
7.1
.
Normal
form
of
logical
operators
.
7.2
.
Mixvalued
logic
.
7.3
.
General
logical
mappings
.
7.4
.
Two
practical
examples

8
.
Logical
matrix
,
fuzzy
set
and
fuzzy
logic
.
8.1
.
Matrices
of
general
logical
variables
.
8.2
.
Logical
operators
for
kvalued
matrices
.
8.3
.
Fuzzy
sets
.
8.4
.
Mappings
over
fuzzy
sets
.
8.5
.
Fuzzy
logic
and its
computation

9
.
Fuzzy
relational
equation
.
9.1
.
kvalued
matrix
and
fuzzy
relational
equations
.
9.2
.
Structure
of the
set
of
solutions
.
9.3
.
Solving
fuzzy
relational
equation
.
9.4
.
Numerical
examples

10
.
Fuzzy
control
with
coupled
fuzzy
relations
.
10.1
.
Multiple
fuzzy
relations
.
10.2
.
Fuzzy
control
of
coupled
multiple
fuzzy
relations
.
10.3
.
Numerical
solution
for
fuzzy
control
design

11
.
Representation
of
boolean
functions
.
11.1
.
Boolean
functions
in
Galois
field
[symbol]
.
11.2
.
Polynomial
form
of
boolean
functions
.
11.3
.
Walsh
transformation
.
11.4
.
Linear
structure
.
11.5
.
Nonlinearity
.
11.6
.
Symmetry
of
boolean
function
. ;
8
12
.
Decomposition
of
logical
functions
.
12.1
.
Disjoint
bidecomposition
.
12.2
.
Nondisjoint
bidecomposition
.
12.3
.
Decomposition
of
multivalued
logical
functions
.
12.4
.
Decomposition
of
mixvalued
logical
functions

13
.
Boolean
calculus
.
13.1
.
Boolean
derivatives
.
13.2
.
Boolean
differential
equations
.
13.3
.
Boolean
integral

14
.
Lattice
,
graph
, and
universal
algebra
.
14.1
.
Lattice
.
14.2
.
Isomorphic
lattices
and
sublattices
.
14.3
.
Matrix
expression
of
finite
lattice
.
14.4
.
Distributive
and
modular
lattices
.
14.5
.
Graph
and its
adjacency
matrix
.
14.6
.
Vector
space
structure
of
graph
.
14.7
.
Planar
graph
and
coloring
problem
.
14.8
.
Universal
algebra
.
14.9
.
Latticebased
logics

15
.
Boolean
network
.
15.1
. An
introduction
.
15.2
.
Fixed
points
and
cycles
.
15.3
.
Invariant
subspace
and
inputstate
description
.
15.4
.
Higherorder
boolean
networks
.
15.5
.
Dynamicstatic
boolean
networks

16
.
Boolean
control
system
.
16.1
.
Dynamics
of
boolean
control
networks
.
16.2
.
Controllability
.
16.3
.
Observability
.
16.4
.
Disturbance
decoupling
.
16.5
.
Some
other
control
problems

17
.
Game
theory
.
17.1
. An
introduction
to
game
theory
.
17.2
.
Infinitely
repeated
games
.
17.3
.
Local
optimization
of
strategies
and
local
Nash/subNash
equilibrium

18
.
Multivariable
polynomials
.
18.1
.
Matrix
expression
of
multivariable
polynomials
.
18.2
.
Differential
form
of
functional
matrices
.
18.3
.
Conversion
of
generators
.
18.4
.
Taylor
expansion
of
multivariable
functions
.
18.5
.
Fundamental
formula
of
differential
.
18.6
.
Lie
derivative

19
.
Some
applications
to
differential
geometry
and
algebra
.
19.1
.
Calculation
of
connection
.
19.2
.
Contraction
of
tensor
field
.
19.3
.
Structure
matrix
of
finitedimensional
algebra
.
19.4
.
Twodimensional
algebras
.
19.5
.
Threedimensional
algebras
.
19.6
.
Lowerdimensional
Lie
algebra
and
invertible
algebra
.
19.7
.
Tensor
product
algebra

20
.
Morgan's
problem
.
20.1
.
Inputoutput
decomposition
.
20.2
.
Problem
formulation
.
20.3
.
Numerical
expression
of
solvability

21
.
Linearization
of
nonlinear
control
systems
.
21.1
.
Carleman
linearization
.
21.2
.
First
integral
.
21.3
.
Invariance
of
polynomial
system
.
21.4
.
Feedback
linearization
of
nonlinear
control
system
.
21.5
.
Single
input
feedback
linearization
.
21.6
.
Algorithm
for
nonregular
feedback
linearization

22
.
Stability
region
of
dynamic
systems
.
22.1
.
Stability
region
.
22.2
.
Stable
submanifold
.
22.3
.
Quadratic
approximation
.
22.4
.
Higher
order
approximation
.
22.5
.
Differentialalgebraic
system
.
Publisher
World Scientific Pub. Co.
Subject
Operator theory.
Matrices.
Spectral theory (Mathematics)
Identifier
9789814374699
(electronic
bk.)
;
9814374687
;
9789814374682
;
http://www.worldscientific.com/worldscibooks/10.1142/8323#t=toc
Language
eng
Type
Electronic books.
FormatExtent
xxii, 587 p. : ill.
Date
c2012
.
OCLC number
874498077
CONTENTdm number
407
Tags
Add tags
for An introduction to semitensor product of matrices and ITS applications
View as list

View as tag cloud

report abuse
Comments
Post a Comment
for
An introduction to semitensor product of matrices and ITS applications
Your rating was saved.
you wish to report:
Your comment:
Your Name:
...
Back to top
Select the collections to add or remove from your search
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Select All Collections
E
Ebook Collection
EReference
ETDA Publications
I
ISEAS (Institute of Southeast Asian Studies)
R
Rare books
S
Somdet Phra Nyanasamvara
Special project (Bachelor of Arts Program in Journalism and Mass Communication)
T
Thailand Research Fund (TRF)
Thammasat History Collection
Thammasat University Research
Thammasat University Textbooks
Thammasat University Theses
The 2011 Flood at TU
The Foundation for the Promotion of Social Sciences and Humanities
The Thai Democratization Center
W
Wat Bowonniwet Vihara Cremation Collection
500
You have selected:
1
OK
Cancel