How is matrix multiplication commutative?
2007-05-01 11:16:34 · 5 answers · asked by Florida Girl 1 in Science & Mathematics ➔ Mathematics
sorry I meant how is it NOT
2007-05-01 13:29:34 · update #1
Matrix multiplication is not commutative.
Matrix A times matrix B = C
While matrix B times matrix A = D
2007-05-01 11:19:24 · answer #1 · answered by kamcrash 6 · 2⤊ 0⤋
Matrix multiplication is not commutative (that is, AB ≠ BA), except in special cases. It is easy to see why: you cannot expect to switch the proportions with the vectors and get the same result. It is also easy to see how the order of the factors determines the result when one knows that the number of columns in the proportions matrix has to be the same as the number of rows in the vectors matrix: they have to represent the same number of vectors.Although matrix multiplication is not commutative, the determinants of AB and BA are always equal (if A and B are square matrices of the same size).
This notion of multiplication is important because if A and B are interpreted as linear transformations (which is almost universally done), then the matrix product AB corresponds to the composition of the two linear transformations, with B being applied first.
2007-05-01 11:20:17 · answer #2 · answered by Nikki 6 · 1⤊ 0⤋
If you mean, "cumulative", then this would be multiplication upon multiplication like in the Matrix movie. Agent Smith clones himself many times over in a cumulative fashion. You can also call it additive multiplication. Just ask the Oracle.
2007-05-01 11:21:22 · answer #3 · answered by leesa 4 · 0⤊ 2⤋
It most definitely is not.
2007-05-01 11:18:20 · answer #4 · answered by bruinfan 7 · 2⤊ 0⤋
It's Not Duh
2007-05-01 11:19:18 · answer #5 · answered by shamlik996 2 · 0⤊ 1⤋