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Similar matricies

by daniel_i_l
Tags: matricies, similar
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daniel_i_l
#1
Jun21-07, 05:52 AM
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P: 867
1. The problem statement, all variables and given/known data
Prove or disprove the following statement:
If A is a singular matrix (detA=0) the it's similar to a matrix with a row of zeros.


2. Relevant equations



3. The attempt at a solution
I know that A has an e-value 0 which means that it's similar to a matrix that has a column of zeros but how do I relate that to the rows?
Thanks.
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mjsd
#2
Jun21-07, 06:28 AM
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P: 860
ok, note that det (M) = product of eigenvalues of M
matt grime
#3
Jun21-07, 07:02 AM
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P: 9,396
Since det(A)=0, there is a row relation.

Or, consider what you do know. A^t has det 0, so there is an M with

(MA^tM^-1)

a matrix with a column of zeroes.

Now how do we get A back out again?


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