01. Inverse of AB and A-transpose
02. A = LU (no row exchanges)
03. Operations of Eliminations
04. Permutation Matrix Family
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
