END 210 - Linear Algebra For Industrial Engineering

Course Objectives

I. To use a mathematically correct language and notation for the applications of Linear Algebra.
II. To develop computational proficiency involving procedures in Linear Algebra.
III. To understand the axiomatic structure of a modern mathematical subject and learn to construct simple proofs.
IV. To solve industrial engineering problems using Linear Algebra.

Course Description

Linear Equations and Matrices: Linear systems of equations, matrices, matrix product, algebraic properties of matrix operations, special matrices (square, symmetric, orthogonal, triangular, diagonal, etc.); Solving Linear Systems: Echelon form of a matrix and its rank, solving linear systems, elementary matrices, matrix inverses, equivalent matrices; Determinants: Definition and properties of the determinant, cofactor expansion and finding the inverse of a matrix, applications of the determinant, Cramer’s rule; Real Vector Spaces: Vectors in two- and three-dimensional spaces, definition of a vector space, subspaces, spanning, linear independence, basis, dimension, orthonormalization (Gram-Schmidt process), projection matrix; Eigenvalues and eigenvectors: Diagonalization and the matrix power, positive definite and semi-definite matrices, the Singular Value Decomposition.