need to solve this equation

[Roshdy]

((xT. A . x)^2) * x = b

A : matrix M*M (known constant)
b : vector M*1 (known constant)

x : vector M*1 (unknown)
xT: the transpose of x

solve for x as a function of A,b

thanks

 

[shivamrules]

this looks incorrect since xT A x is 1*1 matrix
its square is also 1*1
then we cant multiply it with x which is M*1 matrix..
so plz chek up ur question..or this may be the soln..

 

[Roshdy]

right, ((xT. A . x)^2) is 1*1 matrix (scaler), the scaler can be multiplied by the vector, the problem is that this scaled is a function of the unknown variable.
thanks

 

[steve10]

Answer:

Since ((xT. A . x)^2) * x = b and ((xT. A . x)^2) is a scalar, we have ((xT. A . x)^2) * xT = bT.

Therefore,
(((xT. A . x)^2) * xT).A.(((xT. A . x)^2) * x)=bT.A.b,
which means
(xT. A . x)^5=bT.A.b,

or
(xT. A . x)^2=(bT.A.b)^(2/5)

Now, from the original equation ((xT. A . x)^2) * x = b, we obtain

x=b/((xT. A . x)^2)=b*(bT.A.b)^(-2/5).