Linear Algebra geniuses come in...

[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

 

[toekramp]

Neo!

 

[moomoo40moo]

I thought you were talking about the movie. *leaves thread*

 

[Xyclone]

[Neo]Woah[/Neo]

 

[JohnCU]

Originally posted by: moomoo40moo
I thought you were talking about the movie. *leaves thread*

 

[KLin]

Do your own @#$@#$@ homework you lazy @#$(@#( son of a @!$(@#$(@ !@#!^&.

 

[HamburgerBoy]

There's a movie called Linear Algebra?

 

[blustori]

Originally posted by: JohnCU

Originally posted by: moomoo40moo
I thought you were talking about the movie. *leaves thread*

I can try to solve this problem for days and still wouldn't be able to.

 

[Xyclone]

You changed the name! Ban! :thumbsdown:

 

[blustori]

OMFG!!! I see a pattern! If I get this I derserve to be at MIT!

 

[Howard]

I don't remember what 'k' is. Refresh my memory, please.

 

[RGUN]

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.

 

[hytek369]

Originally posted by: HamburgerBoy


There's a movie called Linear Algebra?

haha

 

[OdiN]

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.

 

[blustori]

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.

 

[Chaotic42]

Prove that it has an inverse (and therefore is not singular).

 

[Howard]

If you want the prog to calculate the det of a given 3x3 or 4x4 matrix, hit me up tomorrow morning.

 

[Juno]

you really need to see a math tutor.

 

[Hyperion042]

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.

 

[kogase]

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.

Yes, I concur.

 

[alphatarget1]

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

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.