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- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/04%3A_R/4.03%3A_Lines_and_PlanesWe can use the concept of vectors and points to find equations for arbitrary lines in Rn, although in this section the focus will be on lines in R3.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/04%3A_R/4.06%3A_Subspaces_and_BasesThe goal of this section is to develop an understanding of a subspace of Rn.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/03%3A_Linear_Transformations_and_Matrix_Algebra/3.02%3A_One-to-one_and_Onto_TransformationsThis page discusses the concepts of one-to-one and onto transformations in linear algebra, focusing on matrix transformations. It defines one-to-one as each output having at most one input and outline...This page discusses the concepts of one-to-one and onto transformations in linear algebra, focusing on matrix transformations. It defines one-to-one as each output having at most one input and outlines examples and theorems related to this property. The text emphasizes that a transformation is onto if every output corresponds to some input.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/05%3A_Linear_Transformations/5.05%3A_One-to-One_and_Onto_TransformationsThis section is devoted to studying two important characterizations of linear transformations, called One to One and Onto.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/07%3A_Vector_Spaces/7.11%3A_The_Matrix_of_a_Linear_TransformationYou may recall from Rn that the matrix of a linear transformation depends on the bases chosen. This concept is explored in this section, where the linear transformation now maps from one arbitrary v...You may recall from Rn that the matrix of a linear transformation depends on the bases chosen. This concept is explored in this section, where the linear transformation now maps from one arbitrary vector space to another.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_IV%3A_Multivariable_Calculus/01%3A_Differentiation_of_Functions_of_Several_Variables/1.06%3A_Directional_Derivatives_and_the_GradientA function z=f(x,y) has two partial derivatives: ∂z/∂x and ∂z/∂y. These derivatives correspond to each of the independent variables and can be interpreted as instantaneous rates of change ...A function z=f(x,y) has two partial derivatives: ∂z/∂x and ∂z/∂y. These derivatives correspond to each of the independent variables and can be interpreted as instantaneous rates of change (that is, as slopes of a tangent line). Similarly, ∂z/∂y represents the slope of the tangent line parallel to the y-axis. Now we consider the possibility of a tangent line parallel to neither axis.