MATH116 Lecture Notes - Lecture 3: Orthogonal Matrix, Linear Algebra, Row And Column Spaces
3 Jul 2017
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Column 1 plus column 2 equals column 3. A wonderful theorem of linear algebra says that the three rows are not independent either. The third row must lie in the same plane as the rst two rows. Some combination of rows 1 and 2 will produce row 3. In the end i had to use elimination to discover that the right combination uses 2 times row 2, minus row 1. Elimination is the simple and natural way to understand a matrix by producing a lot of zero entries. A further goal is to understand how the matrix acts. When a multiplies x it produces the new vector ax. The whole space of vectors moves it is transformed by a. Special transformations come from particular matrices, and those are the foundation stones of linear algebra: diagonal matrices, orthogonal matrices, triangular matrices, symmetric matrices. The eigenvalues of those matrices are special too.
