Linear Algebra
Object 'Linear Algebra' belongs to the 'Branches Of Math' theme.Connection to Real Analysis:
Analysis is chock-full of vector spaces, often infinite-dimensional ones such as function spaces and functional spaces.
Connection to Abstract Algebra:Linear algebra is strictly a subset of abstract algebra. Nonetheless, it's worth mentioning that in a certain sense, vector spaces are "perverse" in an algebraic sense: vectors and scalars can't be added to each other, a lurid state of affairs sure to vex any universal algebraist.
To many students, an encounter with the notion of linear transformations in an elementary linear algebra course is the first sampling of the rich beauty of homomorphisms in general.
Connection to Set Theory:To many students, an encounter with the notion of linear transformations in an elementary linear algebra course is the first sampling of the rich beauty of homomorphisms in general.
The Axiom of Choice from set theory is indispensable in advanced linear algebra: it is the key to proving the general existence of vector spaces of higher dimension.
Connection to Graph Theory:Graph theorists use matrices to encode data about their graphs, and then the full arsenal of linear algebra can be applied toward optimizing graph theoretical computations. This happy marriage of theories has a very real effect on all of our lives; every time you search a query in Google, linear algebra and graph theory conspire to give you the best results.
Connection to Model Theory:Some of the notions in linear algebra (such as the span of a set of vectors), which the undergraduate already finds quite general and abstract, are actually generalized much further in model theory.
No connections to an additional 5 objects.Click here to Edit the connections between Linear Algebra and other objects.(or you can Add a New Object)