Gopi, E: MATHEMATICAL SUMMARY FOR DIGIT

1. Matrices. 1-1 Properties of vectors. 1-2 Properties of Matrices. 1-3 LDU Decomposition of the arbitrary matrix. 1-4 PLDU Decomposition of the arbitrary matrix. 1-5 Vector space and its properties. 1-6 Linear independence, Span, Basis and the Dimension of the Vector Space. 1-7 Four Fundamental Vector spaces of the Matrix. 1-8 Basis of the Four Fundamental Vector spaces of the Matrix. 1-9 Observations on the Results of the Example 1-12. 1-10 Vector Representation with different basis. 3-11 Linear transformation of the vector. 1-12 Transformation matrix with different basis (Similar Matrices). 3-13 Orthogonality. 1-14 System of Linear Equation. 1-15 Solutions for the system of Linear Equation [A] x = b. 1-16 Gram-Schmidt Orthogonalization procedure for obtaining orthonormal basis. 1-17 QR Factorization. 1-18 Eigen values and the Eigen Vectors. 1-19 Geometric Multiplicity (vs) Algebraic Multiplicity. 1-20 Diagonalization of the matrix. 1-21 Schur's Lemma. 1-22 Hermitian Matrices. 1-23 Unitary Matrices. 3-24 Normal Matrices. 1-25 Applications of Diagonalization of the non-deficient matrix. 1-26 Singular Value Decomposition(SVD). 1-27 Applications of Singular Value Decomposition.2. Probability. 2-1 Introduction. 2-2 Axioms of Probability. 2-3 Class of Events or Field(F). 2-4 Probability Space (S,F,P). 2-5 Probability measure. 2-6 Conditional Probability. 2-7 Total Probability Theorem. 2-8 Bayes Theorem. 2-9 Independence. 2-10 Multiple Experiments. 2-11 Random Variable. 2-12 Cumulative Distribution Function(cdf) of the random variable 'x'. 2-13 Continuous Random variable. 2-14 Discrete Random variable. 2-15 Probability mass function. 2-16 Probability density function. 2-17 Two Random variables. 2-18 Conditional distributions and densities. 2-19 Independent Random variables. 2-20 Some Important results on conditional density function. 2-21 Transformation of the Random variables of the type Y=g(X). 2-22Transformation of the Random variables of the type Y1=g1(X1,X2),

From the reviews:"Summarizes the mathematical background required for the study of digital signal processing. ... The material is presented in a concise outline format, with relatively brief explanations illustrated by simple numerical examples. ... This volume may be useful to advanced students in electrical engineering and other areas of science and engineering who need to review these mathematical subjects before studying digital signal processing. Summing Up: Recommended. Upper-division undergraduates and graduate students." (B. Borchers, Choice, Vol. 48 (5), January, 2011)