The Desnanot-Jacobi Identity and Proof of Correctness of The Condensation Algorithm
The proof that the condensation method computes the determinant of the matrix if no divisions by zero are encountered is based on an identity known as the Desnanot-Jacobi identity.
Let be a square matrix, and for each denote by the matrix that results from by deleting the -th row and the -th column. Similarly, for denote by the matrix that results from by deleting the -th and -th rows and the -th and -th columns.
Read more about this topic: Dodgson Condensation
Famous quotes containing the words identity, proof, correctness and/or condensation:
“An identity would seem to be arrived at by the way in which the person faces and uses his experience.”
—James Baldwin (1924–1987)
“If any proof were needed of the progress of the cause for which I have worked, it is here tonight. The presence on the stage of these college women, and in the audience of all those college girls who will some day be the nation’s greatest strength, will tell their own story to the world.”
—Susan B. Anthony (1820–1906)
“With impressive proof on all sides of magnificent progress, no one can rightly deny the fundamental correctness of our economic system.”
—Herbert Hoover (1874–1964)
“Entification begins at arm’s length; the points of condensation in the primordial conceptual scheme are things glimpsed, not glimpses.”
—Willard Van Orman Quine (b. 1908)