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Algebra

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3 Dec 2008 23:28:38 IST

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Trace of a Matrix

None

A,B,C are three nxn matrices then :

Trace(ABC) =

a)Trace(CBA)

b)Trace(ACB)

c)Trace(BAC)

Answer : Trace(CBA)

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Comments (6)

shrey

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Joined: 21 Aug 2008

Posts: 78

3 Dec 2008 23:33:00 IST

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can u explain the ques to me...wat is trace of a matrix??

disha ahuja

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Joined: 1 Nov 2008

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3 Dec 2008 23:36:59 IST

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sum of diagonal elements in a square matrix is called trace.

shrey

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Joined: 21 Aug 2008

Posts: 78

3 Dec 2008 23:45:36 IST

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wat is the meaning of trace(ABC)???

can anyone explain? plzz

disha ahuja

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3 Dec 2008 23:51:21 IST

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it means multiplication of square matrices ABC nd trace of the square matrix so obtained i.e sum of diagonal elements

Sagar Saxena

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Joined: 8 Oct 2008

Posts: 7221

4 Dec 2008 17:23:02 IST

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hello dear..

sum of diagonal elements in a square matrix is called trace.

ABC = CAB = BCA ,this follow a circular law..of matrix multiplication

nudge me if iam wrong.........

Aniruddh Padia

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Joined: 4 Dec 2008

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5 Dec 2008 02:21:22 IST

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Im sorry sagar but thats wrong .... matrix multiplication doesnt follow that law.

And 'aatman' the options and the answer both are wrong.

There is a property in trace for three matrices that is the order of a matrix is changed without changing the position of the individual matrices with respect to each other the trace of a matrix remains unchanged.

What i mean is trace(ABC) = trace(CAB)= trace (BCA) .... im not interchangin any 2 positions here .... im just advancing the cycle of the matrix like we do in scalar triple product of vectors.

So here you can also verify that u wont get any of your options by substituting any 3 non singular matrices and u will find out that only Trace(ABC) = Trace (CAB) = Trace (BCA).

if im unclear nudge me ....

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