| 1 |
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Group, Ring, Field, Vectors and Vector Spaces |
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| 2 |
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Supspaces, Inner Product Spaces and Metric properties |
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| 3 |
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Linear Independence, Basis, Dimension, Matrix Vector Spaces, Basis and Dimension of Matrices |
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| 4 |
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Multiplication of Matrices, Transposition, Inverse Matrix, Special Matrices |
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| 5 |
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Elementary Operations in Matrices and Their Applications |
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| 6 |
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Trace and its properties, Coordinates and Transition matrix in vector spaces. |
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| 7 |
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Linear transformations, Rank and kernel of linear transformation, Dimension theorem |
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| 8 |
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MID-TERM EXAM |
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| 9 |
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Relation between Linear transformations and matrices |
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| 10 |
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Determinant function, Properties of a determinant function, Calculation of the determinant of a matrix |
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| 11 |
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Adjoint matrix, Applications of determinant (linear independence, rank of matrix, cross product, mixed product) |
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| 12 |
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Linear Equation Systems |
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| 13 |
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Eigenvalues and eigenvectors of matrices, characteristic equation and polynomial, |
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| 14 |
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Cayley Hamilton Theorem and Applications |
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| 15 |
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FINAL EXAM |
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| 16 |
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FINAL EXAM |
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| 17 |
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FINAL EXAM |
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