Bounds on the extremal eigenvalues of positive definite matrices.
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Date
2018
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Abstract
The minimum and maximum eigenvalues of a positive de nite matrix are crucial to
determining the condition number of linear systems. These can be bounded below and
above respectively using the Gershgorin circle theorem. Here we seek upper bounds for
the minimum eigenvalue and lower bounds for the maximum eigenvalue. Intervals containing
the extremal eigenvalues are obtained for the special case of Toeplitz matrices.
The theory of quadratic forms is discussed in detail as it is fundamental in obtaining
these bounds.
Description
Master’s degree. University of KwaZulu-Natal, Durban.