This course equips students with fundamental Linear Algebra techniques and their application in solving systems of linear equations, determining the basis and dimension of vector spaces, and calculating and utilizing eigenpairs. It also introduces students to working with non-numerical objects, particularly vectors and matrices.

Apply fundamental Linear Algebra techniques in various engineering applications:

• Solve systems of linear equations using various methods, work with matrices, and determine the determinant of a matrix (C3).
• Apply vector concepts in Euclidean spaces R2R^2R2, R3R^3R3, and RnR^nRn, as well as general vector spaces and their properties, including transformations in R2R^2R2 and R3R^3R3 (C3).
• Calculate eigenvalues, eigenbases, inner products, diagonalization, orthogonal matrices, and orthogonal diagonalization, addressing problems related to orthogonality (C3).
• Apply linear transformation concepts in general vector spaces, including finding kernels, ranges, inverse transformations, composition, isomorphism, and similarity (C3).

• Systems of Linear Equations and Matrices

  • Solving systems of linear equations
  • Matrix operations and properties

• Determinants

  • Calculation of determinants
  • Properties and applications of determinants

• Euclidean Vector Spaces

  • Concepts of vectors and vector spaces
  • Geometry of Euclidean spaces

• General Vector Spaces

  • Abstract vector spaces and their properties
  • Basis and dimension

• Eigenvalues and Eigenvectors

  • Finding eigenvalues and eigenvectors
  • Applications in linear transformations

• Inner Product Spaces

  • Definitions and properties of inner products
  • Orthogonality and projections

• Diagonalization

  • Diagonalizing matrices
  • Applications of diagonalization

• General Linear Transformations

  • Understanding linear transformations
  • Properties and matrix representations

1. Elementary Linear Algebra, Howard Anton & Anton Kaul, 12th edition, 2019