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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Winter 2004 • Question 2

Question

Math 6610 • Analysis of Numerical Methods I Winter 2004 • Question 2

Frobenius Norm The Frobenius Norm \(\lVert A\rVert _F\) of an \(n\times n\) matrix \(A\) is defined by \[ \lVert A\rVert _F= \sqrt {\sum _{i=1}^n\sum _{j=1}^n a_{ij}^2}. \tag {4} \] Let \(H=I-2uu^T\) be a Householder reflection as in the preceding problem and compute the Frobenius Norm of \(H\).

Raw LaTeX

{Frobenius Norm}
The Frobenius Norm \(\lVert A\rVert_F\) of an \(n\times n\) matrix \(A\) is defined by
\[
  \lVert A\rVert_F=
  \sqrt{\sum_{i=1}^n\sum_{j=1}^n a_{ij}^2}. \tag{4}
\]
Let \(H=I-2uu^T\) be a Householder reflection as in the preceding problem and compute
the Frobenius Norm of \(H\).

Topic Tags

Linear Programming and Optimization Matrix Norms and Induced Norms QR Factorization