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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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Algebra of sets, Transformations, Some algebraic structures, Permutation, polynomials
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R1-Chapter 1
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2
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Definitions and some basic concepts, equation of matrixs, sum of matrixs, multiplication of matrix by a scalar, matrix multiplication, application of matrix multiplication, multiplication of matrixs
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R1-Chapter 2
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3
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Multiplication of matrixs, Transposition of a matrix, Some special matrixs, Some relations with special matrixs, Trace and properties of a square matrix, Inverse matrixs, Zero dividing matrixs
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R1-Chapter 2
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4
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Elementary operations, Elementary matrixs
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R1-Chapter 3
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5
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calculate of inverse of an inverse matrix with elementary row operations, equivalent matrixs and applications
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R1-Chapter 3
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6
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Elementary properties of determinants, Calculation of determinants with minors, Permutations and determinants, Determinant of a product
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R1-Chapter 4
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7
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Sarrus rule, adjoint of a square matrix, the existence of inverse matrix by the block separation method, Permanents and their properties
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R1-Chapter 4
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8
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Definitions, systems of linear equations and matrixs, rank of a matrix
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R1-Chapter 5
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9
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Finding the rank of a matrix with elementary row operations, Criteria related to the existence of the solution of systems of linear equations, Solution of systems of linear equations, Solution of systems of homogeneous equations
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R1-Chapter 5
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10
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Definition of vector spaces and some elementary properties, Sub-vector spaces, Linear dependence and Linear independence, Base and dimension
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R1-Chapter 6
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11
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Coordinates of a vector according to a base, Row and column rank, The relation between the rank and determinant of a square matrix
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R1-Chapter 6
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12
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Inner product, vector norms, distance between two vectors, angle between two vectors, orthogonal vectors
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R1-Chapter 7
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13
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Characteristic polynomial, eigenvalue and eigenvector, eigenspace, finding the inverse of a square matrix with the help of Cayley-Hamilton theorem, estimation of the eigenvalues of a square matrix with the help of the matrix norm, singular values
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R1-Chapter 9
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14
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Similar matrixs, Diagonalization, Some applications of diagonalization, Diagonalization of symmetric matrixs
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R1-Chapter 10
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