Let T be the linear map on defined by

Determine the matrix of T with respect to the basis of .

What are the eigenvalues of T? Is T diagonalisable?

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- Mar 9th 2008, 06:16 AMDeadstarlinear maps
Let T be the linear map on defined by

Determine the matrix of T with respect to the basis of .

What are the eigenvalues of T? Is T diagonalisable? - Mar 9th 2008, 09:23 AMPlato
I will help with the basic matrix.

From we get the matrix

- Mar 9th 2008, 10:50 AMCaptainBlack
- Mar 9th 2008, 11:11 AMDeadstar
cheers guys. One more question, what does the symbol that looks like a "U to the power 'an upside down T'" mean? I dont know how to notate that with latex.

- Mar 9th 2008, 11:58 AMChloroform
lol, you miss those lectures too? I'm doing the same course.

The 'U to the power 'an upside down T' thing you speak of is the orthogonal complement of U. The orthogonal compliment of a subspace U of an inner product V is the set of all vectors in V that are orthogonal to every vector in U.

Know Q3 yet? :p - Mar 9th 2008, 12:09 PMDeadstar
no ive not really looked at it yet, Q.1s sorted. Trying to do the Stats assignment as well, bloody hard...

- Mar 9th 2008, 06:39 PMlllll
For

is invertible?

& would ? - Mar 9th 2008, 09:01 PMCaptainBlack
No is not invertible, the matrix of has zero determinant.

Another way to look at it is that if it were invertibable then for every quadratic function (quadratic function here means a polynomial of degree not more than 2):

would be a unique quadratic, but it is neither unique nor always a quadratic

(put to see that it is not always a quadratic)

RonL