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Exercise 11.10.1

Avg difficulty 3.0

Compute the following complex dot products in Cn\mathbb{C}^{n}:

(a)[1i]⋅[1+i2],(b)[21i]⋅[i1−3],(c)[i1−3]⋅[21i],(d)[ii+11]⋅[1+2i−2−i].(a)\left[\begin{array}{c}1\\ i\end{array}\right]\boldsymbol{\cdot}\left[\begin{array}{c}1+i\\ 2\end{array}\right],\quad(b)\left[\begin{array}{c}2\\ 1\\ i\end{array}\right]\boldsymbol{\cdot}\left[\begin{array}{c}i\\ 1\\ -3\end{array}\right],\quad(c)\left[\begin{array}{c}i\\ 1\\ -3\end{array}\right]\boldsymbol{\cdot}\left[\begin{array}{c}2\\ 1\\ i\end{array}\right],\quad(d)\left[\begin{array}{c}i\\ i+1\\ 1\end{array}\right]\boldsymbol{\cdot}\left[\begin{array}{c}1+2i\\ -2\\ -i\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Inner product spaces, Complex inner product spaces, Exercise 11.10.1

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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.