6/9/2023 0 Comments Linear algebra by khan academy![]() ![]() Because an isomorphism preserves linear structure, two isomorphic vector spaces are "essentially the same" from the linear algebra point of view, in the sense that they cannot be distinguished by using vector space properties. When V = W are the same vector space, a linear map T : V → V is also known as a linear operator on V.Ī bijective linear map between two vector spaces (that is, every vector from the second space is associated with exactly one in the first) is an isomorphism. Linear algebra is the branch of mathematics concerning linear equations such as:Ī 1 x 1 + ⋯ + a n x n = b, The blue line is the common solution to two of these equations. ![]() In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. ![]()
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