Thread: Converting A Function to Matrix...?

Hey guys,

Iv been given the function:

V(x,y) = kx^2 + k[(y-x)^2] + ky^2

They say :

Write down a symetric matrix A such that V = (X^T)AX where X = (x,y)^T

T: Transpose of matrix.

Whaaaat the helll???

Thanks.

Originally Posted by outspired

Hey guys,

Iv been given the function:

V(x,y) = kx^2 + k[(y-x)^2] + ky^2

They say :

Write down a symetric matrix A such that V = (X^T)AX where X = (x,y)^T

T: Transpose of matrix.

Whaaaat the helll???

Thanks.

The want you to find a symmetric matrix such that:



Multiplying out that matrix product gives you . So what do need to be in order to make the equation hold? Remember that has to be symmetric.

Thanks man, i did something like that but it didnt come out like that. You just need to take the co-effients of the equation and match it with the equation determined by the multiplication....by the way, how did you know they were looking for a 2x2?

a = 2k

b+c = -2k => b=c=-k

d = 2k

Originally Posted by outspired

Thanks man, i did something like that but it didnt come out like that. You just need to take the co-effients of the equation and match it with the equation determined by the multiplication....by the way, how did you know they were looking for a 2x2?

a = 2k

b+c = -2k => b=c=-k

d = 2k

Because of the rules governing matrix multiplication. We were multiplying



To multiply the first two, must be . To multiply the second pair, must be .

Wow...i never saw it that way.

Thanks alot man...you've just given me 3 minutes of extra sleep...JOY.