Where Does Matrix Multiplication Come From? What AB Represents

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:ArialMT;color:#000000;} .ft02{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} Where does matrix multiplication come from? What AB Represents The product AB represents the transformation B followed by transformation A. That is acounterintuitive concept, which we are accustomed to writing from left to right. Unfortunately, matrices are defined by rules that require multiplication from right to left. Ifyou think about it, when you write a function f times a different function g, what you'rereally saying is apply g, then f. Multiplying matrices is done in reverse order from that usedin standard mathematical notation. If, for example, I write AB times X, where X is some vector that I want to transform, it's thesame as A times BX. The associative property is a good property of well-behaved products. Therefore, matrixproduct is associative. This means that we can reorder the factors in a product ABXwithout changing the result. We can start with BX or we can start with AB. BX means applying transformation B to X,and multiplying by A means applying transformation A. We first apply B, then we applyA—or we can apply them both at once: AB.