how to maximize the two-norm of one vector?

Hi everyone,

I am trying to solve one equation: Ax=b

where A is a 4*3 non-rectangular matrix, x is the 3*1 unknown vector and b is the 3*1 vector.

I know if the minimum two norm sum of x, i.e. sqrt(x(1)^2+x(2)^2+x(3)^2), is wanted, then the solution is

x=pinv(A)*b, where pinv(A) is the pseudo-inverse matrix of A, that meets pinv(A)*A=A*pinv(A)=I, where I

is the identity matrix.

On the contrast, if the maximum two norm sum of x is wanted, how should I do it ?

Thanks very much !

Answer 1

[Stanley Cheng]

Sorry A is a 2*3 non-rectangular matrix...

Answer 2

[Torsten]

Your problem is unbounded in x.

Thus it does not have a solution.

Best wishes

Torsten.