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Syllabus of Linear Algebra- Vector space, Linear dependence of vectors, Basis, Dimension, Linear transformations, Matrix representation with respect to an ordered basis, Range space and null space, Rank-nullity theorem, Rank and inverse of a matrix, Determinant, Solutions of system of linear equations, Consistency conditions, Eigenvalues and eigenvectors, Cayley-Hamilton theorem, Symmetric, Skew-symmetric, Hermitian, Skew-Hermitian, Orthogonal and unitary matrices.

Massachusetts Institute of Technology (MIT), United States, Harvard University, Stanford University, University of Cambridge, United Kingdom, University of Oxford, University of California, Berkeley (UCB), Princeton University, ETH Zurich (Swiss Federal Institute of Technology), Switzerland, University of California, Los Angeles (UCLA), New York University (NYU)