B.Sc. (Data Science) Linear Algebra Syllabus - Mumbai University
This is the SY BSc Data Science syllabus under NEP 2020, in force from the academic year 2025-26. The University still sets the earlier Choice Based papers alongside it for ATKT candidates, so check which scheme your exam form names before you revise.
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Syllabus for Linear Algebra
Module I: Algebra of Matrices: Introduction and operations on matrices
- Systems of linear equations: Linear Equations, System of linear equations, Homogeneous and Non-Homogeneous linear systems, Equivalent systems, Solution of linear systems- Triangular form, Echelon form, Gaussian elimination method, Gauss Jordan method, Vector equations, The matrix equation Ax = b.
- Field: Definition, examples - 𝑅, 𝐶, GF(2).
- Vectors: Vector addition, Scalar-vector multiplication, Combining vector addition and scalar multiplication, Dot product.
- Vector Spaces: Definition, examples, linear combinations, Span, Subspace, Row space, Column space, linear dependence and linear independence, basis and dimension.
Module II: Linear Transformations: Definition, examples, Kernel and Image of a linear
- mapping, Null space, Rank and nullity dimension theorem, Algebra of linear transformations.
- Linear Transformation and Matrices: Matrix representation of a linear transformation, Change of Basis, Similarity.
- Inner Product Spaces & Orthogonality – Introduction, Inner product Spaces, Examples, Properties, Orthogonality, Orthogonal Sets, Orthonormal Sets, Gram-Schmidt Orthogonalization process.
- Determinants – Introduction, Properties of the Determinant, Formulas for the Determinant, Applications of Determinants.
- Diagonalization, Eigenvalues and Eigenvectors: Introduction, Characteristic polynomial, Definition and computation of eigen values and eigenvectors, Properties of eigenvalues and eigenvectors, Cayley-Hamilton theorem, Minimal polynomial, Derogatory matrices, Similarity of matrices, Diagonalization of matrices, Jordan canonical forms.
Textbooks
- 1 Lipschutz, S., & Lipson, M. (2018). Linear Algebra (4th ed.)., Schaum’s Outlines - McGraw Hill
- 2 Klein, P. (2013). Coding the Matrix Linear Algebra through Applications to Computer Science (1st ed.)., Newtonian Press
- 3 Lay, S., & Lay, C., & Macdonald, J. (2016). Linear Algebra and Its Applications (5th ed.)., Pearson Education
- 4 Davis, E., & Peters, A. (2012). Linear Algebra and Probability for Computer Science Applications (1st ed.)., CRC Press
- 5 Strang, G. (2007). Linear Algebra and Its Applications (4th ed.)., Cengage Learning
- 1 Singh, K. (2014). Linear Algebra: step by step (1st ed.)., Oxford University Press
- 2 Knop, L. (2008). Linear Algebra: A First Course with Applications (1st ed.)., CRC Press
- 3 Little, J., & Damiano, D. (2011). A Course in Linear Algebra (1st ed.)., Dover Publications
- 4 Cohn, P. (2017). Elements of Linear Algebra (1st ed.)., CRC Press
- 5 Singh, A. (2014). Elements of Computation Theory (1st ed.)., Springer
- 6 Hopcroft, E., Motwani, R., & Ullman, J. (2008). Introduction to Automata Theory, Languages, and Computation (3rd ed.)., Pearson Education
Reproduced from the University of Mumbai syllabus for B.Sc. (Data Science) under NEP 2020, in force from the academic year 2025-26. Wording is as printed in that syllabus. Module numbering is as printed there too.
The complete syllabus
This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.