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)
Famous quotes containing the word matrix:
“The matrix is God?
In a manner of speaking, although it would be more accurate ... to say that the matrix has a God, since this beings omniscience and omnipotence are assumed to be limited to the matrix.
If it has limits, it isnt omnipotent.
Exactly.... Cyberspace exists, insofar as it can be said to exist, by virtue of human agency.”
—William Gibson (b. 1948)