Hermitian problem I need some help

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In summary, the problem asks to prove that if A and B are hermitian matrices, then their sum (A+B)^n is also hermitian. This is based on the property that a hermitian matrix is equal to its conjugate, and by extension, the sum and product of two hermitian matrices are also hermitian.
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thebigstar25
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Homework Statement



Prove that if A and B are hermitian, so is (A+B)^n


Homework Equations



if an operator is hermitian then it is equal to its conjugate (A= A+)



The Attempt at a Solution



im pretty much bad when it comes to math, any hints would be appreciated ..
thanks in advance..
 
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  • #2
What else do you know about hermitian matrices? For example, is the sum of two hermitian matrices hermitian? What about their product?
 
  • #3
vela said:
What else do you know about hermitian matrices? For example, is the sum of two hermitian matrices hermitian? What about their product?

thanks a lot for the help vela .. I will try from there .. :)
 

1. What is a Hermitian problem?

A Hermitian problem is a mathematical problem that involves finding the eigenvalues and eigenvectors of a Hermitian matrix. A Hermitian matrix is a square matrix that is equal to its own conjugate transpose. These types of problems are common in quantum mechanics and other areas of physics.

2. How is a Hermitian problem solved?

To solve a Hermitian problem, one can use methods such as diagonalization, which involves finding a basis of eigenvectors for the matrix, or the Rayleigh quotient iteration method, which involves finding the eigenvalues and eigenvectors through a series of approximations.

3. What are the applications of Hermitian problems?

Hermitian problems have many applications in physics, such as in quantum mechanics, where they are used to solve for the energy levels of a system. They are also used in engineering, signal processing, and other fields that involve linear algebra and complex numbers.

4. Are there any special properties of Hermitian matrices?

Yes, Hermitian matrices have several special properties. They are always diagonalizable, meaning they can be transformed into a diagonal matrix with only non-zero entries on the main diagonal. They also have real eigenvalues and orthogonal eigenvectors, making them useful for solving various types of problems.

5. What is the difference between a Hermitian problem and a non-Hermitian problem?

The main difference between a Hermitian problem and a non-Hermitian problem is that a Hermitian problem involves a Hermitian matrix, while a non-Hermitian problem involves a matrix that is not equal to its own conjugate transpose. This difference leads to different methods and techniques for solving these types of problems.

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