The eigenvalues of a 4x4 matrix, A, are 5, 3, 3, and 1. Execute Gram-Schmidt process on the following two vectors to find an orthonormal basis set: (5, 0). After Vi = (2, 2) , v2 = normalization, we have two new vectors u1 = (x1, Y1) and U2 (x2, Y2). What is the trace, i.e. sum of the diagonal entries, of the matrix A?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 8BEXP
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The eigenvalues of a 4x4 matrix, A,
are 5, 3, 3, and 1.
Execute Gram-Schmidt process on the
following two vectors to find an
orthonormal basis set:
Vị
(2,2), v2 =
(5, 0). After
normalization, we have two new
(x1, Y1) and
(x2, Y2).
vectors u1
U2
What is the trace, i.e. sum of the
diagonal entries, of the matrix A?
What is the second largest eigenvalue
of A??
Transcribed Image Text:The eigenvalues of a 4x4 matrix, A, are 5, 3, 3, and 1. Execute Gram-Schmidt process on the following two vectors to find an orthonormal basis set: Vị (2,2), v2 = (5, 0). After normalization, we have two new (x1, Y1) and (x2, Y2). vectors u1 U2 What is the trace, i.e. sum of the diagonal entries, of the matrix A? What is the second largest eigenvalue of A??
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