This course illustrates the nature of mathematics as a blend of technique, theory, and applications. The important problem of solving systems of linear equations leads to the algebra of matrices, determinants, vector spaces, bases and dimension, linear transformations, and Eigen values. Vector spaces are studied in an abstract setting, examining the concepts of linear independence, span, bases, subspaces, and dimension. There follows a discussion of the association between linear transformations and matrices.
Artificial Intelligence 132 CRs
David C. Lay, Steven R. Lay, Judi J. McDonald, Linear Algebra and Its Applications, Pearson.
| content serial | Description |
|---|---|
| 1 | Matrices: Definition - Addition –Scalar multiplication – Matrices with special properties. |
| 2 | Matrix multiplication – Matrix transpose – Determinants. |
| 3 | Matrix inverse. |
| 4 | Systems of linear equations: Linear equations - Reduced Row Echelon Form and Row Operations – Matrix Rank. |
| 5 | Rank and systems of linear equations - The Homogeneous Case. |
| 6 | Systems of linear equations the Non-Homogeneous Case – Criteria for Consistency and Uniqueness. |
| 7 | Criteria for Consistency and Uniqueness. |
| 8 | Vector Spaces: Vector Algebra [definition-addition-multiplication by scalar-dot product- cross product]. |
| 10 | Definitions of vector space and Basic Concepts – Subspaces part 2. |
| 11 | Definitions of vector space and Basic Concepts – Subspaces part 3. |
| 12 | Introduction to Linear Transformations. |
| 13 | Linear Transformations: Mappings - General Properties of Linear Transformations. |
| 14 | Eigenvalues and Eigen. |
| 15 | Diagonalization. |
| 9 | Definitions of vector space and Basic Concepts – Subspaces part 1. |
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