Register to reply

Algebraic multiplicity of matrix

by srinivasanlsn
Tags: algebraic, matrix, multiplicity
Share this thread:
srinivasanlsn
#1
Apr3-12, 02:36 AM
P: 6
hi friends plz help in finding out the ans for this . A 3x3 matrix was given , am asked to find algebraic multiplicity of it !! how to find algebraic multiplicity of 3x3 matrix ??
Phys.Org News Partner Science news on Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
micromass
#2
Apr3-12, 06:27 AM
Mentor
micromass's Avatar
P: 18,323
Did you mean the algebraic multiplicity of an eigenvalue??

Well, how did you define it??
srinivasanlsn
#3
Apr12-12, 04:19 AM
P: 6
the algebraic multiplicity of the matrix a=[ 0 1 0 ]
[ 0 0 1 ]
[ 1 -3 3 ]
a.1
b.2
c.3
d.4

i don get the question first, somebody help me...

srinivasanlsn
#4
Apr12-12, 04:20 AM
P: 6
Algebraic multiplicity of matrix

my next question is how to find determinant of 4x4 matrix ??
srinivasanlsn
#5
Apr15-12, 08:28 AM
P: 6
the algebraic multiplicity of the matrix
[ 0 1 0 ]
[ 0 0 1 ]
[ 1 -3 3 ]

options :
a.1
b.2
c.3
d.4

i don get the question first, somebody help me...
micromass
#6
Apr15-12, 10:40 AM
Mentor
micromass's Avatar
P: 18,323
Again, what is your definition of algebraic multiplicity?
uponit12
#7
Apr24-12, 09:22 PM
P: 2
First rearrange and the answer is obvious.

[1 -3 3]
[0 1 0]
[0 0 1]

From here the eigenvalues are obviously [1,1,1]. From here the question says what is the algebraic multiplicity. The question was obviously used for simplicity, so you know the multiplicity for the eigenvalue 1 is 3 since it appears in the diagonal 3 times.

Since it is the only one the answer can only be C.
AlephZero
#8
Apr25-12, 06:45 AM
Engineering
Sci Advisor
HW Helper
Thanks
P: 7,172
We know what the algebraic multiplicity of an eigenvalue is.

The OP's question was about the algebraic multiplicity of a matrix, which is not a term that I have ever seen before (and neither has Google).

Maybe something got "lost in tanslation" here...
HallsofIvy
#9
Apr25-12, 08:31 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,557
Quote Quote by srinivasanlsn View Post
my next question is how to find determinant of 4x4 matrix ??
To find the determinant of a 4x4 matrix, you could use the basic definition- but that's very difficult. Most people use "expansion by minors".
The determinant of
[tex]\left|\begin{array}{cccc}a & b & c & d \\ e & f & g & h \\ i & j & k & l\\ m & n & o & p\end{array}\right|[/tex]
is given by
[tex]a\left|\begin{array}{ccc}f & g & h \\ j & k & l \\ n & o & p\end{array}\right|- b\left|\begin{array}{ccc}e & g & h \\ i & k & l \\ m & o & p\end{array}\right|+ c\left|\begin{array}{ccc}e & f & h \\ i & j & l\\ m & n & p\end{array}\right|- d\left|\begin{array}{ccc}e & f & g \\ i & j & k \\ n & o & p \end{array}\right|[/tex]
uponit12
#10
Apr25-12, 08:51 AM
P: 2
AlephZero & srinivasanlsn,

Remember this post shows that the person asking is answering a multiple choice question, as everyone is aware, which has a common instructor imposed complication written in, which is: as you mentioned a term which has no direct definition but instead must be understood only be really understanding the term multiplicity as it is used in Linear algebra.

The multiplicity of an eigenvalue λ of a linear transformation T as the number of independent associated eigenvectors. That is, as the dimension of the kernel of T-λ1V. etc, etc...

If the student knows this or something similar then the seemingly confusing terminology is made clear by using the terms interchangeably due to a nesting effect of definitions. Much like the use of dimension of the kernel above could be stated in a more confusing manner like using it to ask the question: what is the dimension of the kernel for A=.....

Not preaching, as nearly all people answering questions knows this already, just telling the person asking to look through the questions by understanding the definitions better.


Register to reply

Related Discussions
Jordan Forms, Algebraic and Geometric Multiplicity Calculus & Beyond Homework 4
Eigenvalues + Algebraic/Geometric Multiplicity Calculus & Beyond Homework 2
Matrix Multiplication and Algebraic Properties of Matrix Operations Calculus & Beyond Homework 2
Algebraic Multiplicity and Eigenspace Precalculus Mathematics Homework 3
Algebraic multiplicity Calculus & Beyond Homework 1