## AI251

### Course Name:

Applied Linear Algebra (AI251)

### Programme:

### Category:

### Credits (L-T-P):

### Content:

Vectors: definition, scalars, addition, scalar multiplication, inner product(dot product), vector projection, cosine similarity, orthogonal vectors, normal and orthonormal vectors, vector norm, vector space, linear combination, linear span, linear independence, basis vectors; Matrices: definition, addition, transpose, scalar multiplication, matrix multiplication, hadamard product, functions, linear transformation, determinant, identity matrix, invertible matrix and inverse, rank, trace, popular type of matrices- symmetric, diagonal, orthogonal, orthonormal, positive definite matrix; Least Squares: Least Square Problem and Solutions; Eigen Values; Eigenvectors: Concept, Significance; Principal Component Analysis: Concept, Properties, Applications; Singular Value Decomposition: Concept, Properties, Applications.