Linear Algebra and Its Applications

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Linear Algebra and Its Applications Fourth Edition Gilbert Strang x y z Ax b y Ay b b 0. z Az 0. 0. Contents Preface iv 1 Matrices and Gaussian Elimination 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. The Geometry of Linear equations . . . . . . . . . . . . . . . . . . . . 4. An Example of Gaussian Elimination . . . . . . . . . . . . . . . . . . 13. Matrix Notation and Matrix Multiplication . . . . . . . . . . . . . . . . 21. Triangular Factors and Row Exchanges . . . . . . . . . . . . . . . . . 36. Inverses and Transposes . . . . . . . . . . . . . . . . . . . . . . . . . . 50. Special Matrices and Applications . . . . . . . . . . . . . . . . . . . . 66. Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72. 2 Vector Spaces 77. Vector Spaces and Subspaces.

Linear algebra moves steadily to n vectors in m-dimensional space. We still want combinations of the columns (in the column space). We still get m equations to produce b (one for each row). Those equations may or may not have a solution. They always have a least-squares solution. The interplay of columns and rows is the heart of linear algebra.

  Applications, Linear, Equations, Algebra, Linear algebra, Linear algebra and its applications