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'''Productum interius''' seu '''productum scalare''' seu '''puncti productum''' est productum duorum [[vector]]um <math> \vec{a} </math> et <math> \vec{b} </math> ubi singulus [[numerus scalaris]] producitur, quid datur formula
:<math> \vec{a} \cdot \vec{b}=\left\|\vec{a}\right\| \, \left\|\vec{b}\right\| \cos \theta \,</math>
Quod productum valorem [[zerum]] attingit cum duo vectores perpendiculares suntsint et maximum, cum duo vectores paralleli suntsint, aequantem [[magnitudo|magnitudines]] duorum vectorum multiplicatos.
 
==Coordinatis orthogonalibus et valoribus realibus ==
 
His vectoribus iuxta basem orthogonalem scriptis
:<math> \vec{a} = \begin{bmatrix} a_1 \\ a_2 \\ a_3 \\ \vdots \end{bmatrix} \, \textit{ et } \;\; \vec{b} = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \\ \vdots \end{bmatrix}</math>,
 
:<math> \langle \vec{a} , \vec{b} \rangle = \vec{a}^T \, \vec{b} = \begin{bmatrix} a_1 \, a_2 \, a_3 \, \dots \end{bmatrix} \begin{bmatrix} b_1 \\ b_2 \\ b_3 \\ \vdots \end{bmatrix} = \sum_{i=1}^n a_i b_i = a_1 b_1 + a_2 b _2 + \cdots + a_n b_n </math>
ubi T denotat [[matrix (mathematica)|transpositionem matricis]], Σ denotat summam arithmeticam et ''n'' est dimensio [[spatium vectoriale|spatii vectorialis]].
 
==Coordinatis orthogonalibus et valoribus complexis ==
 
His autem vectoribus [[numerus complexus|valoribus complexis]] praeditis, productum interius scribi oportet
 
 
== Bibliographia ==
*Anton, Howard. [[1977]]. ''Elementary Linear Algebra.'' Novi Eboraci: John Wiley &amp; Sons.
*Birkhoff, Garrett, et Saunders MacLane. [[1965]]. ''A Survey of Modern Algebra.'' Editio tertia. Novi Eboraci: Macmillan.
*Bourbaki, Nicolas Bourbaki. [[2007]]. ''Algèbre, chapitres 1 à 3'' Éléments de mathematique. Berolini: Springer Verlag.
*Gowers, Timothy, ed. [[2008]]. ''The Princeton Companion to Mathematics.'' Princeton: Princeton University Press. ISBN 978-0-691-11880-2.
*Hart, Roger. [[2011]]. ''The Chinese Roots of Linear Algebra.'' BaltimoreBaltimorae: Johns Hopkins University Press. ISBN 978-0-8018-9755-9.
*Heffron, Jim. [[2011]]. ''Linear Algebra.'' Liber ab auctore editus, [http://joshua.smcvt.edu/linearalgebra/ in reteinterrete.]
 
[[Categoria:Algebra linearis]]
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