Multiplying complex matrices and hermition

[polaris90]

Homework Statement

I have a 4x4 matrix V composed of complex numbers. I also have a 1x4 matrix S. The question asks to solve for c in S = Vc

Homework Equations

I learned that c = <V, S>/||V||^2, or c= (1/a)*<V, S> where "a" is the value of the entries on the main diagonal of the Hermition matrix of V.

The Attempt at a Solution

I don't know how to solve for c because I suppose that S should be a column matrix not a row matrix, unless I transpose it but that hasn't been defined. Some help would be appreciated.

 

[Mark44]

Homework Statement

I have a 4x4 matrix V composed of complex numbers. I also have a 1x4 matrix S. The question asks to solve for c in S = Vc

I think there is a mistake in the problem statement. For Vc to be defined, c has to be 4 X something. If c is 4 X 1, then the product Vc will be 4 X 1.

Homework Equations

I learned that c = <V, S>/||V||^2, or c= (1/a)*<V, S> where "a" is the value of the entries on the main diagonal of the Hermition matrix of V.

The Attempt at a Solution

I don't know how to solve for c because I suppose that S should be a column matrix not a row matrix, unless I transpose it but that hasn't been defined. Some help would be appreciated.

 

[Mark44]

BTW, this should be posted in the Calculus & Beyond section. I am moving this thread to that section.

 

[polaris90]

Thanks for the reply, I was confirmed that the 1x4 should be transposed which solves the problem.