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Exercise 11.10.7

Avg difficulty 3.0

Which of the following vectors, if any, are orthogonal?

u1=[1i0],u2=[1−i1],u3=[01−i],u4=[001].\mathbf{u}_{1}=\left[\begin{array}{c}1\\ i\\ 0\end{array}\right],\quad\mathbf{u}_{2}=\left[\begin{array}{c}1\\ -i\\ 1\end{array}\right],\quad\mathbf{u}_{3}=\left[\begin{array}{c}0\\ 1\\ -i\end{array}\right],\quad\mathbf{u}_{4}=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Inner product spaces, Complex inner product spaces, Exercise 11.10.7

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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.