Using Matrices and Linear Transformations by Charles Cullen (Dover, ISBN 0-486-66328-0).

- Chapter 1

This is notation used by the author that is archaic or otherwise not currently standard; also, notation of my own that I believe to be more consistent or logical than the accepted standard that I've used in the worked solutions.

Author | Standard | Mine | Meaning |

∋ | : | “such that” | |

${\mathcal{F}}_{\U0001d62e\u2a2f\U0001d62f}$ | ${\mathbb{F}}^{\U0001d62e\u2a2f\U0001d62f}$ |
field of m-by-n matrices
| |

$\stackrel{\u0305}{\U0001d63b}$ | $\stackrel{\u0305}{\U0001d63b}$ or ${\U0001d63b}^{*}$ | ${\U0001d63b}^{*}$ | complex conjugate |

${\sum}_{\U0001d62a}$ | ${+}_{\U0001d62a}$ |
summation over i
| |

${ent}_{\U0001d62a\U0001d62b}$ |
$\left[\right]$_{𝘪𝘫} |
the element in the ith row and jth column of 𝗔
| |

$\U0001d5d1$, $\U0001d5b7$, $\U0001d5b7$ | $\U0001d5d1$, $\U0001d605/\stackrel{\u0305}{\U0001d5d1}$, $\U0001d5eb/\U0001d5b7$ | $\U0001d5d1$, $\U0001d605/\stackrel{\u0305}{\U0001d5d1}$, $\U0001d5eb/\stackrel{\u033f}{\U0001d5b7}$ | scalar, vector, matrix |

I welcome any comments or corrections to the solutions.

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