ABSTRACT
This chapter reviews basic linear algebra from a geometric perspective, focusing on intuition and algorithms that work well in the two- and three-dimensional case. It describes both the mechanics of matrix arithmetic and the determinant of "square" matrices, i.e., matrices with the same number of rows as columns. The chapter describes how to use the multiplications to accomplish changes in the vector such as scaling, rotation, and translation. Usually think of determinants as arising in the solution of linear equations. The chapter shows that any symmetric matrix can be diagonalized, or decomposed into a convenient product of orthogonal and diagonal matrices. However, most matrices we encounter in graphics are not symmetric, and the eigenvalue decomposition for nonsymmetric matrices is not nearly so convenient or illuminating, and in general involves complex-valued eigenvalues and eigenvectors even for real-valued inputs.
