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Oscar Lanzi III
science forum Guru Wannabe

Joined: 30 Apr 2005
Posts: 176

Posted: Sun Jul 02, 2006 11:21 am    Post subject: Re: Identity Matrix

Multiplication by an identity matrix looks like nothing, but the
idenbtity matrix enters nontrivially into more complex operations.

The example everyone knows is the equation that determines eigenvalues
of a matrix. Any eigenvalue lambda of a matrix M satisfies the
equation:

det(M-lambda*I) = 0

You can't directly subtract a scalar, lambda, from the matrix M, but
multiplying by I turns lambda into a matrix that functions like the
original scalar.

--OL
Daher Hicham
science forum beginner

Joined: 30 May 2005
Posts: 4

Posted: Sun Jul 02, 2006 10:31 am    Post subject: Re: Identity Matrix

Hello,

The identity matrix is an important tool. I call it a tool and that is
for several reasons. You should keep in mid that matrices are a simple
organisation of numbers. Operations with matrices can reflect
complicated system of equations. The value of the identity matrix is
not only in the fact that it is neutral in multiplications but also it
reduces the time that we need if we look into the system of equation
equation by equation. The identity matrix simplify the work in
inference and econometric work. You can find alot of cases where the
identity matrix reduce the cost of calculus (such in sociology, medical
research....).

Hicha DAHER
brianushman@gmail.com wrote:
 Quote: Hello, and thank you for reading. Hopefully someone can explain what the exact purpose of an Identity Matrix is? If the Identity matrix is I than [I][A] = [A] your output is the same as your input which is why it's called identity. But I do not understand the value of having this... if my input is going to be the same as the output than that seems like a waisted operation.
Gottfried Helms
science forum Guru

Joined: 24 Mar 2005
Posts: 301

Posted: Sun Jul 02, 2006 8:59 am    Post subject: Re: Identity Matrix

Am 02.07.2006 01:56 schrieb NotP:
 Quote: brianushman@gmail.com> wrote in message news:1151798107.555599.272810@m73g2000cwd.googlegroups.com... Hello, and thank you for reading. Hopefully someone can explain what the exact purpose of an Identity Matrix is? If the Identity matrix is I than [I][A] = [A] your output is the same as your input which is why it's called identity. But I do not understand the value of having this... if my input is going to be the same as the output than that seems like a waisted operation. I guess we should get rid of zero, too. I too

<G>
Aage Andersen
science forum beginner

Joined: 12 Jun 2005
Posts: 29

Posted: Sun Jul 02, 2006 7:10 am    Post subject: Re: Identity Matrix

<brianushman@gmail.com> skrev i en meddelelse
 Quote: Hello, and thank you for reading. Hopefully someone can explain what the exact purpose of an Identity Matrix is? If the Identity matrix is I than [I][A] = [A] your output is the same as your input which is why it's called identity. But I do not understand the value of having this... if my input is going to be the same as the output than that seems like a waisted operation.

You can add or subtract I to some other matrix.

Aage
Stephen Montgomery-Smith1
science forum Guru

Joined: 01 May 2005
Posts: 487

Posted: Sun Jul 02, 2006 12:10 am    Post subject: Re: Identity Matrix

brianushman@gmail.com wrote:
 Quote: Hello, and thank you for reading. Hopefully someone can explain what the exact purpose of an Identity Matrix is? If the Identity matrix is I than [I][A] = [A] your output is the same as your input which is why it's called identity. But I do not understand the value of having this... if my input is going to be the same as the output than that seems like a waisted operation.

You want to have some kind of symbol to represent "do nothing." For one
thing, it gives you a point of comparison. So for example, how do you
define the inverse? It is that, when combined with the operation, ends
up with doing nothing.
fishfry
science forum Guru Wannabe

Joined: 29 Apr 2005
Posts: 299

Posted: Sun Jul 02, 2006 12:04 am    Post subject: Re: Identity Matrix

brianushman@gmail.com wrote:

 Quote: Hello, and thank you for reading. Hopefully someone can explain what the exact purpose of an Identity Matrix is? If the Identity matrix is I than [I][A] = [A] your output is the same as your input which is why it's called identity. But I do not understand the value of having this... if my input is going to be the same as the output than that seems like a waisted operation.

Good point. We should get rid of the number 1 for the same reason.
Multiply it by any number and you get back the same number. Who needs it!
NotP

Joined: 05 Sep 2005
Posts: 87

Posted: Sat Jul 01, 2006 11:56 pm    Post subject: Re: Identity Matrix

<brianushman@gmail.com> wrote in message
 Quote: Hello, and thank you for reading. Hopefully someone can explain what the exact purpose of an Identity Matrix is? If the Identity matrix is I than [I][A] = [A] your output is the same as your input which is why it's called identity. But I do not understand the value of having this... if my input is going to be the same as the output than that seems like a waisted operation.

I guess we should get rid of zero, too.
brianushman@gmail.com
science forum beginner

Joined: 01 Jul 2006
Posts: 1

 Posted: Sat Jul 01, 2006 11:55 pm    Post subject: Identity Matrix Hello, and thank you for reading. Hopefully someone can explain what the exact purpose of an Identity Matrix is? If the Identity matrix is I than [I][A] = [A] your output is the same as your input which is why it's called identity. But I do not understand the value of having this... if my input is going to be the same as the output than that seems like a waisted operation.

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