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MSC Semester I -Mathematical Foundations for Data Science
Updated on Sep, 2026
Programming, Data Science, Python
Duration - 16.5 hours
Training 5 or more people ?
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Vector Spaces: Vector spaces, Subspaces, Basis and dimension of a vector space, linear
dependence and independence, spanning set. Linear transformation, kemel, range, Matrix
Representation of a linear transformation, rank- nullity theorem, change of basis and similar
matrices Inner-product spaces, orthogonal sets and bases, orthogonal projection, Gram-Schmidt orthogonalization process
Matrices; trace and Rank of a Matrix and their properties, determinants, inverse, symmetric,
orthogonal and idempotent matrices and their properties, Gauss elimination, row canonical
form, diagonal form, triangular form,
Eigenvalue Probtems: characteristic roots and vectors, caley-Hamilton theorem,
Diagonalization ofa Matrix, algebraic and geometric multiplicity ofa characteristic root and
spectral decomposition of a rear symmetric matrix., Singular value Decomposition. GaussJordan-LU decomposition, Singular Value Decomposition,
Quadratic forms: Real quadratic forms (eFs), reduction and classification ofeFs, index and
signature. Simultaneous reduction of two eFs. Extreme form of a eF. Moore-penrose and
generalized inverses and their properties.
Check out the detailed breakdown of what’s inside the course
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