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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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Vector spaces, Matrices, Determinants
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R1. Section 1.1, R1. Section 1.2
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2
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Linear transformations and characteristic values, inner product spaces
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R1. Section 1.3, R1. Section 14
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3
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Elementary operations, determinant of partitioned matrices and the inverse of a sum
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R1. Section 2.1, R1. Section 2.2
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4
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The inverse of the sum of partitioned matrices
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R1. Section 2.3
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5
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Rank of Product and Sum, Eigen values of AB and BA
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R1. Section 2.4
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6
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Commuting Matrices and Matrix Decompositions
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R1. Section 3.1, R1. Section 3.2
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7
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Jordan Canonical form of a matrix
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R1. Section 3.3, R1. Section 3.4
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8
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Numerical Ranges, Matrix Norms, and Special Operations
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R1. Section 4.1, R1. Section 4.2, R1. Section 4.3
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9
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Idempotence, Nilpotence, Involution, and Projections, Tridiagonal Matrices
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R1. Section 5.1, R1. Section 5.2
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10
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Circulant Matrices , Vandermonde Matrices
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R1. Section 5.3, R1. Section 5.4
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11
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Hadamard Matrices, Permutation and Doubly Stochastic Matrices, Nonnegative Matrices
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R1. Section 5.5, R1. Section 5.6, R1. Section 5.7
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12
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Properties of Unitary Matrices, Real Orthogonal Matrices
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R1. Section 5.8, R1. Section 5.9
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13
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Metric Space and Contractions, Contractions and Unitary Matrices
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R1. Section 6.1, R1. Section 6.2, R1. Section 6.3
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14
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The Unitary Similarity of Real Matrices and a Trace Inequality of Unitary Matrices
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R1. Section 6.4, R1. Section 6.5, R1. Section 6.5
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Prerequisites
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-
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Language of Instruction
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English
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Responsible
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Assoc. Prof. Dr. Faruk KARAASLAN
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Instructors
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-
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Assistants
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-
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Resources
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R1. Zhang, F. (1999). Matrix Theory Basic Results and Techniques. Springer-Verlag, New York Berlin Heidelberg.
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Supplementary Book
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SR1. Loehr, N. (2014). Advanced Linear Algebra (Textbooks in Mathematics) 1st Edition. Chapman and Hall/CRC, London.
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Goals
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To teach basic notions and theorems of linear algebra, partitioned matrices and some special type matrices.
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Content
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Elementary linear algebra, Partitioned Matrices, Matrix Polynomials and Canonical forms, Special Matrices, Uniter Matrices and Contractions.
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Program Learning Outcomes |
Level of Contribution |
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1
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Improve and deepen the gained knowledge in Mathematics in the speciality level
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4
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2
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Use gained speciality level theoretical and applied knowledge in mathematics
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3
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3
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Perform interdisciplinary studies by relating the gained knowledge in Mathematics with other fields.
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-
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4
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Analyze mathematical problems by using the gained research methods
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-
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5
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Conduct independently a study requiring speciliaty in Mathematics
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-
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6
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Develop different approaches and produce solutions by taking responsibility to problems encountered in applications
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3
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7
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Evaluate the gained speciality level knowledge and skills with a critical approach and guide the process of learning
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-
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8
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Transfer recent and own research related to mathematics to the expert and non-expert shareholders written, verbally and visually
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-
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9
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Communicate with colleagues written and verbally by mastering a foreign language at least European Language Portfolio B2 General Level
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-
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10
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Make use of the necessary computer softwares and information technologies related to Mathematics
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-
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11
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Have the awareness of acting compatible with social, scientific, cultural and ethical values during the process of collecting, interpreting, applying and informing data related to Mathematics
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-
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