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 can be skipped by readers comfortable with linear algebra. However, there may be some enlightening tidbits even for such readers, such as the development of determinants and the discussion of singular and eigenvalue decomposition. The standard way to manage the algebra of computing determinants is to use a form of Laplace’s expansion. The key part of computing the determinant this way is to find cofactors of various matrix elements. Each element of a square matrix has a cofactor which is the determinant of a matrix with one fewer row and column possibly multiplied by minus one. The adjoint is the transpose of the cofactor matrix, which is just the matrix whose elements have been replaced by their cofactors.
