Unit 1 Vectors

5 lecture hours

• Vectors and geometry in two and three-space dimensions
• Algebraic properties
• Dot products and the norm of a vector
• Important inequalities
• Vector spaces
• subspaces, and vector space axioms
• Complex vector spaces

Unit 2 Independence and orthogonality

7 lecture hours

• Linear independence of vectors
• Basis and dimension of a vector space
• Orthogonal vectors and subspaces
• The Gram-Schmidt orthogonalisation

Unit 3 Matrices

5 lecture hours

• Matrix operations
• Column, row, and null space
• The rank of a matrix
• Inverse and transpose
• Elementary matrices
• The Gauss- Jordan method

Unit 4 Systems of linear equations

7 lecture hours

• Examples of linear systems
• Geometry Program Name: Master of Engineering Level: PG Branch: Computer Engineering (Artificial Intelligence And Data Science) Course / Subject Code : ME01095081 Subject Name : Mathematics for Machine Learning of linear equations
• Gaussian elimination
• Row echelon form
• Homogeneous and nonhomogeneous systems of linear equations
• Application to the intersection of lines and planes

Unit 5 Elementary matrix factorizations and determinants

5 lecture hours

• LU factorization
• related algorithms and operation count
• PLU factorization
• Calculating the determinant of a matrix
• Properties of the determinant of a matrix
• Application examples: area
• volume and cross product

Unit 6 Eigen value decomposition, Singular value decomposition, Principal

• Component Analysis 7 15

Unit 7 Linear transformations

9 lecture hours

• Definition and examples
• Properties and composition of linear transformations
• reflections and stretches
• Translations using homogeneous coordinates
• One-to-one and onto transformations