Multiplying complex matrices and hermition

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Homework Help Overview

The discussion revolves around a problem involving the multiplication of complex matrices, specifically a 4x4 matrix V and a 1x4 matrix S, with the goal of solving for the variable c in the equation S = Vc. Participants are examining the implications of matrix dimensions and the properties of Hermitian matrices in this context.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants express uncertainty about the dimensionality of the matrices involved, particularly questioning whether S should be a column matrix instead of a row matrix. There is also discussion regarding the definition of c and the implications of the Hermitian matrix properties on the solution.

Discussion Status

The conversation includes attempts to clarify the matrix dimensions and the necessary conditions for the equation to hold. One participant suggests that the issue may be resolved by transposing the 1x4 matrix S, which has been confirmed by another participant, indicating a potential direction for resolution.

Contextual Notes

There is a mention of a possible mistake in the problem statement regarding the dimensions of c, which is critical for the matrix multiplication to be defined. Additionally, the thread has been noted for relocation to a more appropriate section of the forum.

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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.
 
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polaris90 said:

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.
polaris90 said:

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.
 
BTW, this should be posted in the Calculus & Beyond section. I am moving this thread to that section.
 
Thanks for the reply, I was confirmed that the 1x4 should be transposed which solves the problem.
 

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