matrices to the power of negative numbers

[gyrag]

I was just wondering why matrices to the power of negative numbers dont give a solution.. is there any theory behind it??

Thanks

 

[stapel]

What do you mean by "dont[sic] give a solution"? How are you defining the meaning of a negative exponent in the context of matrices?

Please be specific. Thank you.

Eliz.

 

[gyrag]

i mean if, on the calculator, i type in the matrix (A)::
(1 -1)
(-1 1)
and then say (A) ^ -2, it gives me a domain error.. what does that mean.. do matrices have 'domains'??

 

[stapel]

Without knowing how your calculator is viewing the negative exponent, and without knowing how your calculator computes inverses (I think), then there is no way for us to know why the calculator is returning the error message you report. My guess would be that the calculator is assuming you mean the square of the inverse, and its algorithm involves dividing by the determinant, which here is zero. But that's only a guess.

Meanwhile, you still haven't said what you mean by the negative square of a matrix. Please define this. Thank you.

Eliz.

 

[pka]

i mean if, on the calculator, i type in the matrix (A)::
(1 -1)
(-1 1)
and then say (A) ^ -2, it gives me a domain error.. what does that mean.. do matrices have 'domains'??

A negative exponent on a matrix says first find the inverse and the raise the inverse to the positive power. In the case you gave, the matrix has no inverse hence the error message.