Lecture 04

01. Inverse of AB and A-transpose

02. A = LU (no row exchanges)

03. Operations of Eliminations

04. Permutation Matrix Family

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01. Inverse of AB and A-transpose

AB_inverse.png

inverse_A_transpose.png

02. A = LU (no row exchanges)

a. A Simple Example

a_simple_example.png

b. Sequence of Elimination and A = LU

sequence.png

c. Why A = LU is preferable than elimination?

why_preferable.png

Because of the conduction effect of elimination, the final elimination matrix E includes an undesirable element in bottom left corner, which does not appear in previous elimination. While in A = LU, multipliers go to L directly(with no row exchanges), which is much simpler than elimination form.

03. Operations of Eliminations

operatin of A.png

Similar to A, the elimination of b can be represented by (N + (N-1) + ... + 1). The computation complexity is square of N.

04. Permutation Matrix Family

permutation.png