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Week
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Topics
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Study Metarials
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1
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Matrices and Systems of Equations: Systems of Linear Equations, Row Echelon Form
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K1-Chapter-1
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2
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Matrix algebra, elementary matrices, separated matrices
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K1-Chapter-1
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3
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Determinants: determinant of a matrix, properties of determinant, Cramer`s rule
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K1-Chapter-2
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4
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Vector spaces: definition and examples, subspaces, linear dependence
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K1-Chapter-3
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5
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Base and dimension, base change, row space and column space
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K1-Chapter-3
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6
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Linear transformations: definition and examples, matrix representation of linear representations, similarity
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K1-Chapter-4
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7
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Orthogonality: scalar product in n-dimensional real space, orthogonal subspaces
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K1-Chapter-5
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8
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Least squares method, inner product spaces, orthonormal sets
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K1-Chapter-5
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9
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Gram-Shmidt orthogonalization process, orthogonal polynomials
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K2-Chapter-6
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10
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Eigenvalues and eigenvectors, diagonalization
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K2-Chapter-8
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11
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Hermit matrices, single value decomposition
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K3-Chapter-7
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12
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Quadratic forms
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K3-Chapter-8
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13
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Positive defined matrices-I
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K3-Chapter-8
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14
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Positive defined matrices-II
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K3-Chapter-10
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