← GATE Mathematics guide GATE Mathematics · Section 2
Linear Algebra
Finite-dimensional vector spaces, canonical forms and quadratic forms — not yet a standalone title in our range.
This section is not yet covered by our M.Sc range — the full syllabus is listed below so your preparation stays complete.
Full syllabus — Section 2
- Finite-dimensional vector spaces over real or complex fields; linear transformations and matrix representations; rank and nullity
- Systems of linear equations; characteristic polynomial; eigenvalues, eigenvectors and diagonalization; minimal polynomial; Cayley–Hamilton theorem
- Finite-dimensional inner product spaces; Gram–Schmidt process; symmetric, Hermitian, normal, orthogonal and unitary matrices; diagonalization by a unitary matrix
- Jordan canonical form; bilinear and quadratic forms
Not in our range yet — Linear Algebra as a standalone M.Sc title — not yet in our range.