Hermitian inner product btw 2 complex vectors & angle btw them

In summary, a Hermitian inner product is a way of measuring similarity between complex vectors by taking the complex conjugate and multiplying it element-wise with the other vector. It allows for the definition of orthogonality and calculation of angles between complex vectors. It cannot be used for non-complex vectors, but can be extended to other types of vectors.
  • #1
raja0088
1
0
What is the relationship btw the Hermitian inner product btw 2 complex vectors & angle btw them.
x,y are 2 complex vectors.
[tex]\theta[/tex] angle btw them

what is the relation btw [tex]x^{H}[/tex]y and cos([tex]\theta[/tex])??
Any help will be good?
 
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  • #2
What is definition of "angle" in complex space? Same as the underlying real space? Then, of course, use the underlying real inner product, which is the real part of the complex inner product.
 

FAQ: Hermitian inner product btw 2 complex vectors & angle btw them

What is a Hermitian inner product?

A Hermitian inner product is a way of measuring the similarity or "closeness" between two complex vectors. It is a generalization of the dot product used for real vectors.

How is a Hermitian inner product calculated?

A Hermitian inner product is calculated by taking the complex conjugate of the first vector and multiplying it element-wise by the second vector. The resulting complex numbers are then summed together to get the inner product value.

What is the significance of a Hermitian inner product?

A Hermitian inner product allows us to define the concept of orthogonality for complex vectors. It also allows us to measure the angle between two complex vectors, which is important in many applications such as signal processing and quantum mechanics.

How is the angle between two complex vectors determined using a Hermitian inner product?

The angle between two complex vectors can be calculated using the formula cosθ = Re(v*w) / ||v|| ||w||, where v and w are the two complex vectors, v* is the complex conjugate of v, and ||v|| denotes the norm of v.

Can a Hermitian inner product be used for non-complex vectors?

No, a Hermitian inner product is only defined for complex vectors. However, the concept of an inner product can be extended to other types of vectors, such as quaternions or matrices.

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