Lesson 1: Introduction and Overview...................2
Lesson 2: Introduction to Matrices.............. 10
Lesson 3: Systems of Linear
... [Show More] Equations.......................23
Lesson 4: Row Reduction and Echelon Forms.................................................................... 36
Lesson 5: Vector Equations................................................................................................. 46
Lesson 6: Matrix Equations................................................................................................. 62
Lesson 7: Solution Sets of Linear Systems.......................................................................... 74
Lesson 8: Linear Independence ........................................................................................... 84
Lesson 9: Linear Transformations....................................................................................... 94
Lesson 10:The Matrix of a Linear Transformation............................................................ 106
Lesson 11: Matrix Operations............................................................................................ 116
Lesson 12: The Inverse of a Matrix ................................................................................... 129
Lesson 13: Characterizations of Invertible Matrices......................................................... 143
Lesson 14: Partitioned Matrices......................................................................................... 157
Lesson 15: Matrix Factorizations....................................................................................... 175
Lesson 16: Iterative Solutions of Linear Systems.............................................................. 192
Lesson 17: Introduction to Determinant ............................................................................ 203
Lesson 18: Properties of Determinants.............................................................................. 219
Lesson 19: Cramer’s Rule, Volume, and Linear Transformations.................................... 234
Lesson 20: Vector Spaces and Subspaces.......................................................................... 245
Lesson 21: Null Spaces, Column Spaces, and Linear Transformations............................ 269
Lesson 22: Linearly Independent Sets; Bases.................................................................... 292
Lesson 23: Coordinate System........................................................................................... 308
Lesson 24: Dimension of a Vector Space .......................................................................... 323
Lesson 25: Rank................................................................................................................. 341
Lesson 26: Change of Basis............................................................................................... 359
Lesson 27: Applications to Difference Equations ............................................................. 366
Lesson 28: Eigenvalues and Eigenvectors......................................................................... 374
Lesson 29: The Characteristic Equation ............................................................................ 384
Lesson 30: Diagonalization................................................................................................ 396
Lesson 31: Eigenvectors and Linear Transformations....................................................... 406
Lesson 32: Complex Eigenvalues...................................................................................... 413
Lesson 33: Discrete Dynamical Systems........................................................................... 419
Lesson 34: Applications to Differential Equations............................................................ 429
Lesson 35: Iterative Estimates for Eigenvalues................................................................. 442
Lesson 36: Revision........................................................................................................... 451
Lesson 37: Revision........................................................................................................... 452
Lesson 38: Inner Product ................................................................................................... 453
Lesson 39: Orthogonal and Orthonormal set..................................................................... 460
Lesson 40: Orthogonal Decomposition ............................................................................. 477
Lesson 41: Orthogonal basis, Gram-Schmidt Process, Orthonormal basis....................... 485
Lesson 42: Least Square Solution...................................................................................... 493
Lesson 43: Inner Product Space......................................................................................... 502
Lesson 44: Application of inner product spaces................................................................ 512
Lesson 45: Revision........................................................................................................... 523 [Show Less]