LINEAR TRANSFORMATIONS LINEAR ALGEBRA , MATHEMATICS

Linear Algebra is a foundational course in mathematics that focuses on the study of vectors, vector spaces, linear transformations, and systems of linear equations. It provides the theoretical and computational tools necessary to understand and solve problems in science, engineering, computer science, economics, and other fields. Course Objectives: Understand the concept of vectors and their operations in 2D, 3D, and n-dimensional space. Solve systems of linear equations using matrix methods. Explore the properties and applications of matrices, including determinants and inverses. Learn about vector spaces and subspaces, basis, and dimension. Analyze linear transformations and their matrix representations. Understand eigenvalues, eigenvectors, and diagonalization. Key Topics Covered: Vectors and vector operations Matrices and matrix algebra Determinants and inverse matrices Systems of linear equations (Gaussian and Gauss-Jordan elimination) Vector spaces and subspaces Basis and dimension Linear transformations Eigenvalues and eigenvectors Orthogonality and least squares Applications: Linear Algebra is widely used in: Machine Learning and Artificial Intelligence Computer Graphics and Cryptography Control Systems and Signal Processing Structural Engineering and Physics This course builds strong analytical and problem-solving skills and is essential for higher studies in mathematics and applied sciences.