Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a sesquilinear form on a complex vector space V is a map V x V -> C that is linear in one argument and antilinear in the other. The name originates from the numerical prefix sesqui- meaning "one and a half". Compare with a bilinear form, which is linear in both arguments; although many authors, especially when working solely in a complex setting, refer to sesquilinear forms as bilinear forms. A motivating example is the inner product on a complex vector space, which is not bilinear, but instead sesquilinear. See geometric motivation below. Conventions differ as to which argument should be linear. We take the first to be conjugate-linear and the second to be linear. This is the convention used by essentially all physicists and originates in Dirac's bra-ket notation in quantum mechanics. The opposite convention is perhaps more common in mathematics but is not universal.

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