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Linear Algebra geniuses come in...

B

blustori

Senior member
How can I prove that the det of an nxn matrix != 0 when each element is defined by w^nk and w = e^-2*pi*j/N where N = the length of the matrix? Hint: the first row and column are all 1's. (I was going to write a program to do this, but then I wouldn't be able to see the pattern.) This is the kind of problem I wish I could solve in a snap.

I am staying up until I get this... with(out) the help of ATOT! I really need this extra credit. TIA
 
why dont you write out a 3x3 and a 4x4 and go from there? they wont take that long to solve and you should be able to recognize any patterns easily enough. I would try and help more but I havent taken linear Algebra in two years.
 
What if the det of an nxn matrix really does = 0 and it's a trick question?


EDIT:

BTW I have no clue what the abbreviations det or nxn mean.

I was lucky to pass pre-calc. Math gets really damn confusing when you're dyslexic.
 
k is the same as n n,k == row, column. The pattern I see is for example
[ 1 1 1 1 ]
[ 1 a b c ]
[ 1 b d e ]
[ 1 c e f ]
hard to explain... I need to look at it more.
 
It's clearly symmetric, therefore it's diagonalizable, therefore its determinant is equal to the product of its eigenvalues, all of which should be positive in that.

...Maybe. That's what I get at first glance.
 
Originally posted by: Hyperion042
It's clearly symmetric, therefore it's diagonalizable, therefore its determinant is equal to the sum of its eigenvalues, all of which should be positive in that.

...Maybe. That's what I get at first glance.
Click to expand...

Yes, I concur.
 
Originally posted by: blustori
How can I prove that the det of an nxn matrix != 0 when each element is defined by w^nk and w = e^-2*pi*j/N where N = the length of the matrix? Hint: the first row and column are all 1's. (I was going to write a program to do this, but then I wouldn't be able to see the pattern.) This is the kind of problem I wish I could solve in a snap.

I am staying up until I get this... with(out) the help of ATOT! I really need this extra credit. TIA
Click to expand...

w^nk where n = the length/width of the matrix? (square, same number)

gotta be more specific... i don't foresee myself solving this problem even though i took that class already. got a C in it.
 
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