(New page: From a large topic called Linear Equation and Matrices, I will focus specifically on Matrix Multiplication and Coordinate Systems. This page is created to enhance the understanding of thes...) |
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| + | '''Matrix Multiplication and Coordinate Systems''' | ||
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From a large topic called Linear Equation and Matrices, I will focus specifically on Matrix Multiplication and Coordinate Systems. This page is created to enhance the understanding of these subtopics for MA 265 students. | From a large topic called Linear Equation and Matrices, I will focus specifically on Matrix Multiplication and Coordinate Systems. This page is created to enhance the understanding of these subtopics for MA 265 students. | ||
| − | 1. Matrix Multiplication | + | '''1. Matrix Multiplication''' |
There are some properties that make matrix multiplication unique and different from other real number multiplication. | There are some properties that make matrix multiplication unique and different from other real number multiplication. | ||
| − | 1.1 Dot Product | + | ''1.1 Dot Product'' |
| − | + | Dot product or inner product of | |
| − | + | ||
| − | is | + | <math>\mathbf{a} = \begin{bmatrix} |
| − | + | a \\ | |
| + | b \\ | ||
| + | c \end{bmatrix}<math> | ||
| + | and | ||
| + | <math>\mathbf{b} = \begin{bmatrix} | ||
| + | d \\ | ||
| + | e \\ | ||
| + | f \\end{bmatrix}</math> | ||
| + | |||
| + | is | ||
| + | <math>\mathbf {a} | ||
| + | \dot | ||
| + | mathbf{b} = ad + be + cf</math> | ||
Revision as of 20:45, 5 December 2010
Matrix Multiplication and Coordinate Systems
From a large topic called Linear Equation and Matrices, I will focus specifically on Matrix Multiplication and Coordinate Systems. This page is created to enhance the understanding of these subtopics for MA 265 students.
1. Matrix Multiplication
There are some properties that make matrix multiplication unique and different from other real number multiplication.
1.1 Dot Product Dot product or inner product of
$ \mathbf{a} = \begin{bmatrix} a \\ b \\ c \end{bmatrix}<math> and <math>\mathbf{b} = \begin{bmatrix} d \\ e \\ f \\end{bmatrix} $
is $ \mathbf {a} \dot mathbf{b} = ad + be + cf $
