Mth415a - Matrix Theory And Linear Estimation

Review of finite dimensional vector spaces (Null space and nullity), Linear dependence and independence, Matrix algebra, Rank of a Matrix, Inverse of a nonsingular matrix. Hermite canonical forms, Generalised inverses, Moore Penrose inverse, solution of linear equations, Projection and orthogonal projection matrices, Idempotent matrices. Real quadratic forms, reduction of pair of real symmetric matrices, Singular value decomposition. Extreme of a quadratic forms, Vector and matrix differentiation. Least squares theory and Gauss Mark off theorem, Cochran's theorem and distribution of quadratic forms, test of single linear hypothesis and more than one hypothesis, ANOVA table, Confidence interval and regions, Power of Ftest. Multiple comparisons and simultaneous confidence intervals.