Modal matrix (linear algebra)
- Modal matrix (linear algebra)
In linear algebra, the modal matrix is used in the diagonalization process involving eigenvalues and eigenvectors.
Assume a linear system of the following form:
:
where "X" is "n"×1, "A" is "n"×"n", and "B" is "n"×1. "X" typically represents the state vector, and "U" the system input.
Specifically the modal matrix "M" is the "n"×"n" matrix formed with the eigenvectors of "A" as columns in "M". It is utilized in
:
where "D" is an "n"×"n" diagonal matrix with the eigenvalues of "A" on the main diagonal of "D" and zeros elsewhere. (note the eigenvalues should appear left→right top→bottom in the same order as its eigenvectors are arranged left→right into "M")
This process is also known as the similarity transform.
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