Question about matrices

[johnjbruin]

Have been thinking about this way too long, cant come up with it
If you have a matrix A = [a1,a2,...,ak]
where [a1,a2,...,ak] are linearly independent column vectors
and let B = At X A

here At means A transpose

then how do you prove that the column vectors of the matrix B are also linearly independent?

 

[Maetryx]

God dang. Try the highly technical forum. I even *took* linear algebra and don't have one clue about your problem. Mid nineties are getting farther and farther away....

 

[johnjbruin]

<< God dang. Try the highly technical forum. I even *took* linear algebra and don't have one clue about your problem. Mid nineties are getting farther and farther away.... >>


yeah i took the linear algebra class also
but this is for a numerical analysis class

I spent a lot of time trying stuff, just couldnt work it out
Come on guys, need some help here.

 

[TCPpacket]

lol, looks like someone else is trying to do their ee103 hw too.

 

[MrDingleDangle]

<< lol, looks like someone else is trying to do their ee103 hw too. >>



dunno about ee103 HW, but my ee113 HW is being a pain in the arse...gonna be long night

 

[johnjbruin]

<< lol, looks like someone else is trying to do their ee103 hw too. >>


yup
you got that right

 

[johnjbruin]

bump
o^o
^
--

 

[knownothingbutphysic]

I think you are talking about square matrices, right?

"column vectors of A are linearly independent" is equivalent to det[A] != 0

det[At] = det[A]
det(B] = det[At] * det[A] = (det[A])^2 != 0

So the column vectors of the matrix B are also linearly independent.

 

[johnjbruin]

hmmm, not allowed to used determinants

 

[wiggyryder]

Step by step...

1. Get At.
2. Multiply At by A to get B.
3. Set [B|0].
4. Use reduce row echelon on B.
5. If you get trivial solutions, then B is linearly independent.

 

[johnjbruin]

<< Step by step...

1. Get At.
2. Multiply At by A to get B.
3. Set [B|0].
4. Use reduce row echelon on B.
5. If you get trivial solutions, then B is linearly independent. >>


This is not for a specific matrix. Need a general solution for all matrices A.

 

[SpecialEd]

Ahhh... i love alegbra... been out of school for more than a year so I can't help you... but this thread definitely brings me back to the days of college...