An Application
Diagonalization can be used to compute the powers of a matrix A efficiently, provided the matrix is diagonalizable. Suppose we have found that
is a diagonal matrix. Then, as the matrix product is associative,
and the latter is easy to calculate since it only involves the powers of a diagonal matrix. This approach can be generalized to matrix exponential and other matrix functions since they can be defined as power series.
This is particularly useful in finding closed form expressions for terms of linear recursive sequences, such as the Fibonacci numbers.
Read more about this topic: Diagonalizable Matrix
Famous quotes containing the word application:
“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Courage is resistance to fear, mastery of fear—not absence of fear. Except a creature be part coward it is not a compliment to say it is brave; it is merely a loose application of the word. Consider the flea!—incomparably the bravest of all the creatures of God, if ignorance of fear were courage.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)