IND 210E - Linear Algebra for Indust.Eng.

Course Objectives

I. To use the correct mathematical language and notation in Linear Algebra applications.
II. To become proficient in computations involving Linear Algebra methods.
III. To understand the axiomatic structure of an important field of modern mathematics and to learn how to construct simple proofs.
IV. To solve Industrial Engineering problems using Linear Algebra.

Course Description

Linear Equations and Matrices: Systems of linear equations, matrices, matrix multiplication, algebraic properties of matrix operations, special types of matrices (square, symmetric, diagonal, triangular, etc.);
Solution of Linear Systems: Row echelon form and rank of a matrix, solution of linear systems, elementary matrices, inverse of a matrix, equivalent matrices;
Determinants: Definition and properties of determinants, cofactor expansion and matrix inverse, other applications of determinants, Cramer’s Rule;
Real Vector Spaces: Vectors in the plane and three-dimensional space, definition of vector space, subspaces, span, linear independence, basis, dimension, orthonormalization (Gram-Schmidt Method), projection matrix;
Eigenvalues and Eigenvectors: Diagonalization and powers of a matrix, positive and semi-positive definite matrices, Singular Value Decomposition (SVD).