![]() ![]() ![]() Quantum mechanics in Hilbert space (2nd ed.). '5.1 Definitions and basic properties of inner product spaces and Hilbert spaces'. 221â∲26, GoogleEprint and as an extract, D. ^ Benjamin Peirce (1872) Linear Associative Algebra, lithograph, new edition with corrections, notes, and an added 1875 paper by Peirce, plus notes by his son Charles Sanders Peirce, published in the American Journal of Mathematics v.'A Brief History of Linear Algebra and Matrix Theory'. ^ Strang, Gilbert (July 19, 2005), Linear Algebra and Its Applications (4th ed.), Brooks Cole, ISBN978-0-03-010567-8.^ Banerjee, Sudipto Roy, Anindya (2014), Linear Algebra and Matrix Analysis for Statistics, Texts in Statistical Science (1st ed.), Chapman and Hall/CRC, ISBN978-1420095388.Linear regression, a statistical estimation method.Identity element of scalar multiplicationġ v = v, where 1 denotes the multiplicative identity of F.įunctional analysis mixes the methods of linear algebra with those of mathematical analysis and studies various function spaces, such as L p spaces. There exists an element 0 in V, called the zero vector (or simply zero), such that v + 0 = v for all v in V.įor every v in V, there exists an element â v in V, called the additive inverse of v, such that v + (â v) = 0ĭistributivity of scalar multiplication with respect to vector additionĭistributivity of scalar multiplication with respect to field additionĬompatibility of scalar multiplication with field multiplication (In the list below, u, v and w are arbitrary elements of V, and a and b are arbitrary scalars in the field F.) Axiom The axioms that addition and scalar multiplication must satisfy are the following. The second operation, scalar multiplication, takes any scalar a and any vector v and outputs a new vector av. ![]() The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w. Elements of V are called vectors, and elements of F are called scalars. A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations satisfying the following axioms. ![]()
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