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- https://math.libretexts.org/Courses/Coastline_College/Math_C285%3A_Linear_Algebra_and_Diffrential_Equations_(Tran)/04%3A_R/4.07%3A_The_Dot_ProductThere are two ways of multiplying vectors which are of great importance in applications. The first of these is called the dot product. When we take the dot product of vectors, the result is a scalar. ...There are two ways of multiplying vectors which are of great importance in applications. The first of these is called the dot product. When we take the dot product of vectors, the result is a scalar. For this reason, the dot product is also called the scalar product and sometimes the inner product.
- https://math.libretexts.org/Courses/Lorain_County_Community_College/Book%3A_Precalculus_(Stitz-Zeager)_-_Jen_Test_Copy/11%3A_Applications_of_Trigonometry/11.09%3A_The_Dot_Product_and_ProjectionPreviously, we learned how add and subtract vectors and how to multiply vectors by scalars. In this section, we define a product of vectors.
- https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/1%3A_Vector_Basics/1.6%3A_Lines_and_PlanesOur goal is to come up with the equation of a line given a vector v parallel to the line and a point (a,b,c) on the line.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_384%3A_Foundations_for_Calculus/01%3A_Functions_-_Fundamental_Concepts/1.01%3A_Introduction_to_FunctionsThis section introduces the concept of functions, distinguishing them from general relations. It explains the definition of a function, including the ideas of domain and range. The section covers the ...This section introduces the concept of functions, distinguishing them from general relations. It explains the definition of a function, including the ideas of domain and range. The section covers the concept of the Vertical Line Test to determine if a relation is a function, and provides examples to illustrate these ideas.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/10%3A_Vectors/10.03%3A_The_Dot_ProductThe previous section introduced vectors and described how to add them together and how to multiply them by scalars. This section introduces a multiplication on vectors called the dot product.
- https://math.libretexts.org/Courses/Lorain_County_Community_College/Book%3A_Precalculus_Jeffy_Edits_3.75/11%3A_Applications_of_Trigonometry/11.09%3A_The_Dot_Product_and_ProjectionPreviously, we learned how add and subtract vectors and how to multiply vectors by scalars. In this section, we define a product of vectors.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_370%3A_Precalculus/01%3A_Relations_and_Functions/1.03%3A_Introduction_to_FunctionsThis section introduces the concept of functions, distinguishing them from general relations. It explains the definition of a function, including the ideas of domain and range. The section covers the ...This section introduces the concept of functions, distinguishing them from general relations. It explains the definition of a function, including the ideas of domain and range. The section covers the concept of the Vertical Line Test to determine if a relation is a function, and provides examples to illustrate these ideas.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus/11%3A_Appendix_-_Prerequisite_Function_Material/11.03%3A_A_Brief_Review_of_FunctionsThis section introduces the concept of functions, distinguishing them from general relations. It explains the definition of a function, including the ideas of domain and range. The section covers the ...This section introduces the concept of functions, distinguishing them from general relations. It explains the definition of a function, including the ideas of domain and range. The section covers the concept of the Vertical Line Test to determine if a relation is a function, and provides examples to illustrate these ideas.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/A_First_Course_in_Linear_Algebra_(Kuttler)/04%3A_R/4.07%3A_The_Dot_ProductThere are two ways of multiplying vectors which are of great importance in applications. The first of these is called the dot product. When we take the dot product of vectors, the result is a scalar. ...There are two ways of multiplying vectors which are of great importance in applications. The first of these is called the dot product. When we take the dot product of vectors, the result is a scalar. For this reason, the dot product is also called the scalar product and sometimes the inner product.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/A_First_Course_in_Linear_Algebra_(Kuttler)/04%3A_R/4.07%3A_The_Dot_ProductThere are two ways of multiplying vectors which are of great importance in applications. The first of these is called the dot product. When we take the dot product of vectors, the result is a scalar. ...There are two ways of multiplying vectors which are of great importance in applications. The first of these is called the dot product. When we take the dot product of vectors, the result is a scalar. For this reason, the dot product is also called the scalar product and sometimes the inner product.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/06%3A_Orthogonality/6.04%3A_The_Method_of_Least_SquaresThis page covers orthogonal projections in vector spaces, detailing the advantages of orthogonal sets and defining the simpler Projection Formula applicable with orthogonal bases. It includes examples...This page covers orthogonal projections in vector spaces, detailing the advantages of orthogonal sets and defining the simpler Projection Formula applicable with orthogonal bases. It includes examples of projecting vectors onto subspaces, emphasizes the importance of orthogonal bases, and introduces the Gram-Schmidt process for generating orthogonal bases from sets of vectors.
