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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 2019 • Question 10

Question

Math 6410 • ODE Fall 2019 • Question 10

Show that a real symmetric linear operator has a full set of real orthogonal eigenvectors (even if it has multiple eigenvalues). [Assume that the operator is a matrix acting in \(\mathbb {R}^n\).]

Raw LaTeX

Show that a real symmetric linear operator has a full set of real orthogonal
eigenvectors (even if it has multiple eigenvalues). [Assume that the operator is a
matrix acting in \(\R^n\).]

Topic Tags

Bounded Linear Operators Hilbert Spaces and Orthogonality Linear Systems and Matrix Exponentials Spectral Theory of Operators