Properties of matrix multiplication
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Operations
In mathematics we call an operation a process that we do to one or more mathematical entities to obtain another entity of that type. This is a very general definition, and may seem very vague, but in practice operations are straightforward enough, and simply express what we know very well. For example, addition and multiplication are operations. The reason why we need the concept of an operation is that some of the things we do with and to (real) numbers, for example, cannot be applied to other entitles. So we need to be explicit about the properties of various operations. Associativity An operation is associative if for any three entities A B C doing [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] In this case the bracket is irrelevant and we write [Equation goes here - download the original to see it.]. For example, for real numbers, [Equation goes here - download the original to see it.] It does not matter how we bracket the individual numbers Commutativity An operation , is commutative if [Equation goes here - download the original to see it.] So the order in which the operation is performed does not matter.
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Contents of
Properties of matrix multiplication
1 Operations
2 Associativity of matrix multiplication
3 Matrix multiplication is not commutative
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