1. |
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Introduction, Vectors and matrices |
Administrative annoucements - Vectors and basic operations - Matrices and basic operations - Special matrices |
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Introduction, Vectors and matrices |
Administrative annoucements - Vectors and basic operations - Matrices and basic operations - Special matrices |
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2. |
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Linear equations |
- Matrix-vector representation of linear equations - Elimination methods |
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Linear equations |
- Matrix-vector representation of linear equations - Elimination methods |
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3. |
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Factorization |
Elimination and factorization - Symetric matrices and factorization |
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Factorization |
Elimination and factorization - Symetric matrices and factorization |
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4. |
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Vector spaces and subspaces |
Spaces of vectors - Column spaces of a matrix - Null space of a matrix |
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Vector spaces and subspaces |
Spaces of vectors - Column spaces of a matrix - Null space of a matrix |
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5. |
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Rank of a matrix |
Rank of a matrix - Row reduced form - Solution to Ax=b |
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Rank of a matrix |
Rank of a matrix - Row reduced form - Solution to Ax=b |
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6. |
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Independence, basis and dimension |
Linear independence of vectors - Basis for a space - Dimension of a space - Dimensions of the four fundamental subspaces |
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Independence, basis and dimension |
Linear independence of vectors - Basis for a space - Dimension of a space - Dimensions of the four fundamental subspaces |
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Independence, basis and dimension |
Linear independence of vectors - Basis for a space - Dimension of a space - Dimensions of the four fundamental subspaces |
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7. |
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Orthogonality |
Orthogonality of the four subspaces |
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Orthogonality |
Orthogonality of the four subspaces |
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Orthogonality |
Orthogonality of the four subspaces |
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Orthogonality |
Orthogonality of the four subspaces |
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8. |
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Applications |
Least squares approximations - Orthogonal bases and Gram-Schmidt process |
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Applications |
Least squares approximations - Orthogonal bases and Gram-Schmidt process |
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9. |
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Determinants |
Properties of determinants - Permutations and cofactors |
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10. |
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Cramer's rule |
Solution to Ax=b - Formula for inverse matrix |
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Cramer's rule |
Solution to Ax=b - Formula for inverse matrix |
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11. |
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Eigenvalues |
Definition of eigenvalues and eigenvectors - Properties of eigenvalues and eigenvectors |
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Eigenvalues |
Definition of eigenvalues and eigenvectors - Properties of eigenvalues and eigenvectors |
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Eigenvalues |
Definition of eigenvalues and eigenvectors - Properties of eigenvalues and eigenvectors |
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12. |
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Diagonalization |
Diagonalizing a matrix - Convergence of a matrix series and eigenvalues - Nondiagonalizable matrices |
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Diagonalization |
Diagonalizing a matrix - Convergence of a matrix series and eigenvalues - Nondiagonalizable matrices |
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13. |
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Symmetric matrices |
Eigenvalues and eigenvectors of symmetric matrices - Positive definite matrices |
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14. |
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Similar matrices |
Definition of similar matrices - Jordan form - Singular value decomposition (SVD) |
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Similar matrices |
Definition of similar matrices - Jordan form - Singular value decomposition (SVD) |
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Similar matrices |
Definition of similar matrices - Jordan form - Singular value decomposition (SVD) |
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