Chapter 7 Introduction toIntroductionto Matrices

Chapter 7 Introduction toIntroductiontoMatricesMatrices are of fundamental importance in 3D math, where they are primarily used to describe therelationship between two coordinate spaces. They do this by defining a computation to transformvectors from one coordinate space to Matrix A Mathematical DefinitionIn linear algebra, a matrix is a rectangular grid of numbers arranged our earlier definition of vector as a one-dimensional array of numbers, a matrix maylikewise be defined as atwo-dimensional arrayof numbers. (Thetwoin two-dimensional array comes from the fact that there are rows and columns, and it should not be confused with 2D vec-tors or Matrices .) A vector is an array of scalars, and a matrix is an array of Matrix Dimensions and NotationJust as we defined the dimension of a vector by counting how many numbers it contained, we willdefine the size of a matrix by counting how many rows and columns it contains. Anr cmatrix(read rbyc ) hasrrows andccolumns. Here is an example of a 4 3 matrix:83 This Chapter introduces the theory and application of Matrices .

Let’s look at a 2×2 example with some real numbers: Now for the 3×3 case: And a 3×3 example with some real numbers: Beginning in Section 9.4, we will also use 4×4 matrices.

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