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Functions, mappings, maps, transformations, operators, linear Transformations, singular and non-singular transformations.
Products of the type XTX, XXT, xtdx ATA and AAT where X is a vector, A is a matrix, and D is a diagonal matrix.Types of Matrices, Triangular matrix, Diagonal matrix, Scalar matrix, Identity matrix, Symmetric matrix, Skew-symmetric matrix, Direct Sum, Transpose of a matrix.Congruence, Congruent Transformation, Symmetric matrices, Skew-symmetric matrices, Hermitian matrices, Skew-Hermitian matrices.Determinant, Minor, Cofactor, Evaluation of a determinant by cofactors.Hermitian forms, Conjunctive Hermitian matrices, definite and semi-definite forms.Affine transformations, eigenvectors and their meaning, a linear point transformation Y AX viewed as occurring in three steps.Systems of linear equations.The solution set of the linear system AX 0 is a vector space.Some theorems, adjoint of a matrix, inverse of a matrix.N-vectors, n-space, dot products, m-dot products.Systems of linear equations, matrix solution, augmented matrix, homogeneous and non-homogeneous systems, Cramer's rule, null space.Technique for solving underdetermined systems of linear equations.
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