MATH 1ZC3 Lecture Notes - Lecture 2: Row And Column Vectors, Commutative Property
13 Oct 2016
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We know matrix multiplication often has trouble with commutivity (ab seldom is ba), but the one of the most unexpected examples is the behaviour of row and column vectors. Sure it looks harmless, but since it"s really a 1x3 matrix some interesting things can happen. For instance look what happens if we compute the expression: And matrix multiplication really is taking the inner product of the rows in the left matrix with the columns on the right, so we get: Or if we instead wrote them as column vectors: then: a b b. In fact, this works for any (finite) size vectors. So, this was all about commuting, or lack thereof. Watch out for them, they"re there, just really, really, short. Since each row and column is one element long, this isn"t a complication. Each product is just the product of the relevant numbers:
