Linear
Algebra.
·
Definition
of matrices, Types of matrices, and their properties.
·
Operations
on matrices and their properties.
·
Elementary
row operations and reduced row form (Echelon form)
·
Systems
of linear equations and their solutions using reduced matrix and matrix
inverses.
·
Determinants,
their properties, and a determinant formula for matrix inverse.
·
System
of linear equations and their solutions using Cramer’s rule and using
elementary transformations.
·
Eigenvalues
and eigenvectors and the Hamilton Cayley theorem.
·
Introduction
to fields (Real, complex), vectors, linearly dependent and independent vectors,
basis, and dimension. Dot product, cross product, and their applications.
·
Calculus
of vectors; functions of vectors and their derivatives, gradient, divergence
and curl. The vector differential operator del.
