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I can see that x' means $x^T$ (x transposed) but it's not mentioned in the documentation — where does this notation come from?

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From http://mathworld.wolfram.com/Transpose.html :

Unfortunately, several other notations are commonly used, as summarized in the following table. The notation Aᵀ is used in this work.

Aᵀ — This work; Golub and Van Loan (1996), Strang (1988)

Ã — Arfken (1985, p. 201), Griffiths (1987, p. 223)

A' — Ayres (1962, p. 11), Courant and Hilbert (1989, p. 9)

Matlab/octave

With caveat that A' is Hermitian transpose (transpose + complex conjugate) when A has complex entities, and you need A.' if you want the real transpose. For matrix A with real coefficients both operations are the same.

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