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Baris 27: === Definisi menurut geometri === Dalam [[Ruang Euklides\|ruang Euclidean]] , suatu [[vektor (spasial)\|vektor Euclidean]] adalah sebuah objek geometri yang memiliki baik besaran (''magnitude'') dan [[arah (geometri)\|arah]] (''direction''). Sebuah vektor dapat digambarkan seperti sebuah anak panah. Besarannya adalah panjangnya, sedangkan arahnya adalah yang ditunjuk oleh ujung panah. Besaran vektor '''A''' dilambangkan dengan <math>\\|\mathbf{A}\\|</math>. Produk skalar dua vektor Euclidean '''A''' dan '''B''' didefinisikan sebagai<ref name="Spiegel2009">{{cite book\|author= M.R. Spiegel, S. Lipschutz, D. Spellman\|first1=\|title= Vector Analysis (Schaum’s Outlines)\|edition= 2nd\|year= 2009\|publisher= McGraw Hill\|isbn=978-0-07-161545-7}}</ref> :<math>\mathbf A\cdot\mathbf B = \\|\mathbf A\\|\,\\|\mathbf B\\|\cos\theta,</math> di mana θ adalah [[sudut]] di antara '''A''' dan '''B'''. Baris 156: ===Inner product=== {{main\|Inner product space}} The inner product generalizes the dot product to [[vector space\|abstract vector spaces]] over a [[field (mathematics)\|field]] of [[scalar (mathematics)\|scalars]], being either the field of [[real number]]s <math>\mathbb{R}</math> or the field of [[complex number]]s <math>\mathbb{C}</math>. It is usually denoted by <math>\langle\mathbf{a}\, , \mathbf{b}\rangle</math>. The inner product of two vectors over the field of complex numbers is, in general, a complex number, and is [[Sesquilinear form\|sesquilinear]] instead of bilinear. An inner product space is a [[normed vector space]], and the inner product of a vector with itself is real and positive-definite. Baris 165: This notion can be generalized to [[continuous function]]s: just as the inner product on vectors uses a sum over corresponding components, the inner product on functions is defined as an integral over some [[Interval (mathematics)\|interval]] {{math\|''a'' ≤ ''x'' ≤ ''b''}} (also denoted {{math\|[''a'', ''b'']}}):<ref name="Lipschutz2009" /> :<math>\langle u , v \rangle = \int_a^b u(x)v(x)dx </math> Generalized further to [[complex function]]s {{math\|''ψ''(''x'')}} and {{math\|''χ''(''x'')}}, by analogy with the complex inner product above, gives<ref name="Lipschutz2009" /> :<math>\langle \psi , \chi \rangle = \int_a^b \psi(x)\overline{\chi(x)}dx.</math> ===Weight function===

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