a. Show that if A is positive definite, then A has an LU factorization, A = LU,

Question:

a. Show that if A is positive definite, then A has an LU factorization, A = LU, where U has positive pivots on its diagonal.b. Show that if A has an LU factorization, A = LU, where U has positive pivots on its diagonal, then A is positive definite.

c. Find an LU factorisation of and use it to obtain a Cholesky factorization of A. Compare with Exercise 6.

Data From Exercise 6

Mark each statement. Justify each answer. In each part, A represents an n x n matrix.

If every coefficient in a quadratic form is positive, then the quadratic form is positive definite.

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Linear Algebra And Its Applications

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a. Show that if A is positive definite, then A has an LU factorization, A = LU,

Question:

A = 9 27 18 27 82 51 18 51 49

Step by Step Answer:

a To show that if A is positive definite then A has an LU factorization A LU where U has positive pivots on its diagonal First lets define positive de...View the full answer

Linear Algebra And Its Applications

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