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ContentsChapter 1 Basics of Linear Algebra 11.1 Basic operations of matrices 21.1.1 Addition for matrices 31.1.2 Scalar multiplication of matrix A 41.1.3 Matrix multiplication 51.1.4 Identity matrix 61.1.5 Transposition matrix and conjugate transpose of matrix A1.1.6 Matrix inversion 71.1.7 Symmetries 81.2 Determinants 111.2.1 Determinant definition 111.2.2 Properties of determinants 121.2.3 Cofactor 141.2.4 Cramer's rule 181.3 Elementary operations 211.3.1 Elementary row transformation 211.3.2 Reduced echelon form 231.3.3 Rank of matrix 251.3.4 Solving equations by elementary transformation 261.4 Linear independence 301.5 Exercises 35Chapter 2 Linear Space 402.1 Set and map 402.2 Linear space 412.3 Basis, dimension and coordinates 472.4 Change of basis 582.5 Exercises 62Chapter 3 Normed Linear Space and Inner Product Space 663.1 Normed linear space and matrix norm 66