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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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The module associated with a linear operator, the characteristic polynomial
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R1- Chapter 7
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2
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Cyclic and indecomposable modules
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R1- Chapter 7
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3
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The rational canonical form
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R1- Chapter 7
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4
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Eigenvalues and eigenvectors, geometric and algebraic multiplicities
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R1- Chapter 8
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5
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The Jordan canonical form
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R1- Chapter 8
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6
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Triangularizability and Schur`s theorem, diagonalizable operators
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R1- Chapter 8
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7
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Norm and distance, isometries, orthogonality
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R1- Chapter 9
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8
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Orthogonal and orthonormal sets, the projection theorem, the Riesz representation theorem
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R1- Chapter 9
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9
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The adjoint of a linear operator, orthogonal projections
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R1- Chapter 10
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10
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Unitary diagonalizability, normal operators
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R1- Chapter 10
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11
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Self-adjoint operators, unitary operators and isometries
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R1- Chapter 10
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12
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Positive operators, the polar decomposition of an operator
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R1- Chapter 10
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13
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Bilinear forms, the matrix of a bilinear form, quadratic forms
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R1- Chapter 11
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14
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Orthogonal complements and ortogonal direct sums
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R1- Chapter 11
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