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Exercise 11.10.9

Avg difficulty 3.0

Consider C3\mathbb{C}^{3} with the complex dot product. Let

v1=[0i2]andv2=[11+i3i+2]\mathbf{v}_{1}=\left[\begin{array}{c}0\\ i\\ 2\end{array}\right]\quad\text{and}\quad\mathbf{v}_{2}=\left[\begin{array}{c}1\\ 1+i\\ 3i+2\end{array}\right]

Use the Gram-Schmidt procedure to find an orthogonal basis for span⁡{v1,v2}\operatorname{span}\left\{\mathbf{v}_{1},\mathbf{v}_{2}\right\}. Then find an orthonormal basis.

Selinger, Matrix Theory and Linear Algebra, Inner product spaces, Complex inner product spaces, Exercise 11.10.9

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.