Matrix Theory (GATE ST) — GATE Statistics (ST) Prep

Subspaces of ℝ𝑛 and ℂ𝑛, span, linear independence, basis and dimension, row space and column space of a matrix, rank and nullity, row reduced echelon form, trace and determinant, inverse of a matrix, systems of linear equations; Inner products in ℝ𝑛 and ℂ𝑛, Gram-Schmidt orthonormalization; Eigen values and eigen vectors, characteristic polynomial, Cayley-Hamilton theorem, symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal, unitary matrices and their eigen values, change of basis matrix, equivalence and similarity, diagonalizability, positive definite and positive semi-definite matrices and their properties, quadratic forms, singular value decomposition.

• Exam: GATE Statistics (ST)
• Section: Matrix Theory

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