Introduction to Linear Algebra
Vector spaces, bases, dimension. Linear transformations, kernel, image, projections and direct sum. Matrices. Gaussian elimination. Inner product. Spectral theorem for self-adjoint operators. Orthogonal and anti-symmetric operators. Pseudo-inverse, quadratic forms and quadratic surfaces. Determinants. Characteristic polynomial. Complex vector spaces, triangular form. Spectral theorem for normal, hermitian and unitary operators. Nilpotent operators. Jordan canonical form.
References:
LIMA, E.L. – Álgebra Linear, Coleção Matemática Universitária, IMPA, 1995.
HALMOS, P.R. – Finite Dimensional Vector Spaces, Ed. Van Nostrand, Princeton, New Jersey, 1958.
LIMA, E.L. – Álgebra Linear, Coleção Matemática Universitária, IMPA, 1995.
HALMOS, P.R. – Finite Dimensional Vector Spaces, Ed. Van Nostrand, Princeton, New Jersey, 1958.
