Complex matrix to Block Matrix

In summary, the speaker is looking to redefine their complex matrix into a block matrix with real and imaginary parts in order to use a solver that only works with real matrices. They want to find eigenvectors and eigenvalues of the new matrix, which is also complex. The matrix element is an integral that is complex, and they are hoping to find a normalization for the real and imaginary parts of the matrix in order to simplify the diagonalization process. However, the question cannot be answered without more specific information and complex calculations may be more useful for this problem.
  • #1
Gaso
4
0
How can I redefine my Complex matrix to a Block matrix, similar as matrix representation of complex number.
I need a Real an Imaginary part as real numbers, to find eigenvalues and eigenvectors with my solver, which works only with Real matrices.

My matrix element is:
[tex]M_{mn}=\int^{tk}_{0} -i Exp[i E_{mn} t] V_{mn}(t) dt[/tex]
The integrals are easy to write, but are complex.
I want to write matrix M as new matrix of dimension 2N to find eigenvectors and eigenvalues of that matrix, which are also complex.
 
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  • #2
We basically have the situation ##M=A+iB##. In order to diagonalize ##M## or to use some normal form, we need to know something about the components ##A## and ##B##. If we find a normalization for ##A##, it could well ruin the structure of ##B## and vice versa. So in any case, the question isn't answerable in this generality. Moreover, complex calculations are usually better than real ones, since we have more eigenvalues available.
 

What is a complex matrix?

A complex matrix is a rectangular array of complex numbers, where each element can have a real and imaginary part. It can be represented in the form of a square matrix, where the diagonal entries are the real numbers and the off-diagonal entries are the imaginary numbers.

What is a block matrix?

A block matrix is a special type of matrix where the entries are themselves matrices. It can be represented in the form of a block, where each block is a sub-matrix. This allows for the manipulation of multiple matrices at once, making it useful in solving complex problems.

What is the difference between a complex matrix and a block matrix?

The main difference between a complex matrix and a block matrix is that a complex matrix consists of complex numbers as elements, while a block matrix consists of matrices as elements. Additionally, a complex matrix is a single matrix, while a block matrix is made up of multiple sub-matrices.

How is a complex matrix converted to a block matrix?

To convert a complex matrix to a block matrix, the complex matrix is divided into smaller sub-matrices, with each sub-matrix becoming a block in the block matrix. This is done by grouping the elements of the complex matrix into their respective blocks, based on their positions in the matrix.

In what applications is a complex matrix to block matrix conversion useful?

A complex matrix to block matrix conversion is useful in many scientific fields, such as physics, engineering, and computer science. It is commonly used in solving systems of linear equations, signal processing, and data compression. It also has applications in quantum mechanics, where complex matrices are used to represent quantum states, and block matrices are used to represent composite systems.

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