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In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors.The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.
Concerning general linear maps, linear endomorphisms, and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other parts of mathematics.
Khan Academy is an American non-profit [3] educational organization created in 2006 by Sal Khan. [1] Its goal is to create a set of online tools that help educate students. [ 4 ] The organization produces short video lessons. [ 5 ]
Normally, a matrix represents a linear map, and the product of a matrix and a column vector represents the function application of the corresponding linear map to the vector whose coordinates form the column vector. The change-of-basis formula is a specific case of this general principle, although this is not immediately clear from its ...
Banerjee, Sudipto; Roy, Anindya (June 6, 2014), Linear Algebra and Matrix Analysis for Statistics (1st ed.), CRC Press, ISBN 978-1-42-009538-8 Beauregard, Raymond A.; Fraleigh, John B. (1973), A First Course In Linear Algebra: with Optional Introduction to Groups, Rings, and Fields , Boston: Houghton Mifflin Company , ISBN 0-395-14017-X
Instructional videos from Khan Academy Introduction to bases of subspaces; Proof that any subspace basis has same number of elements "Linear combinations, span, and basis vectors". Essence of linear algebra. August 6, 2016. Archived from the original on 2021-11-17 – via YouTube. "Basis", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
1 Linear equations. 2 Matrices. 3 Matrix decompositions. 4 Relations. 5 Computations. 6 Vector spaces. 7 Structures. ... This is an outline of topics related to ...
In the mathematical fields of linear algebra and functional analysis, ... [3] [proof 1] that ... (Khan Academy) This page was last ...
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