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Linear algebra concerns vector spaces whether finite- or infinite-dimensional. Abstract algebra, or modern algebra, includes linear algebra, along with many other kinds of objects, such as groups, rings, fields, lattices, and so on. In part, it was an attempt to put mathematics on a more rigorous footing.

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Q: What is the difference between abstract algebra and linear algebra?

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Differential equations, Linear Algebra, Abstract Algebra, Real and Complex Analysis, Advanced Calculus, and lots of other fun stuff.

Example: Algebra will show you how quickly the gallon will fill over time. Calculus will show you how quickly the gallon will fill over time while it is also being slowly drained.

It isn't; the algebra 1 and 2 that you get taught in middle or high school is elementary algebra. When (if you want to) you get into more advanced algebra, you can learn linear algebra (matrix algebra) and abstract algebra (which involves sets, operations on sets, groups, and many more concepts), and probably several more types of algebra I've never heard of.

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They are not alternative solutions so that we can compare them. Relational database (which is based on relational algebra) demands (atleast the founder of relational database Codd suggests) that the query language follow linear syntax. The linear syntax languages don't rely up on newline characters as terminators of expressions or statements -- instead they rely on other tokens such as semicolon or comma and so on.

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yes, also this question belongs in the linear algebra forum not the abstract algebra forum

Linear Algebra is a special "subset" of algebra in which they only take care of the very basic linear transformations. There are many many transformations in Algebra, linear algebra only concentrate on the linear ones. We say a transformation T: A --> B is linear over field F if T(a + b) = T(a) + T(b) and kT(a) = T(ka) where a, b is in A, k is in F, T(a) and T(b) is in B. A, B are two vector spaces.

Linear algebra is restricted to a limited set of transformations whereas algebra, in general, is not. The restriction imposes restrictions on what can be a linear transformation and this gives the family of linear transformations a special mathematical structure.

Differential equations, Linear Algebra, Abstract Algebra, Real and Complex Analysis, Advanced Calculus, and lots of other fun stuff.

Yutze Chow has written: 'Modern abstract algebra' -- subject(s): Abstract Algebra 'Linear signal-flow graphs and applications' -- subject(s): Electronics, Flowgraphs, Graphic methods

Example: Algebra will show you how quickly the gallon will fill over time. Calculus will show you how quickly the gallon will fill over time while it is also being slowly drained.

"Algebra" by Michael Artin is a classic. "Abstract Algebra" by Dummit and Foote is also great. Technically D&F is a graduate level book, but that's just because it contains so much content (it's over 1000 pages!). One can easily learn undergraduate level algebra from it by only studying the appropriate sections. For linear algebra I recommend Axler's Linear Algebra Done Right.

Many problems in economics can be modelled by a system of linear equations: equalities r inequalities. Such systems are best solved using matrix algebra.

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It isn't; the algebra 1 and 2 that you get taught in middle or high school is elementary algebra. When (if you want to) you get into more advanced algebra, you can learn linear algebra (matrix algebra) and abstract algebra (which involves sets, operations on sets, groups, and many more concepts), and probably several more types of algebra I've never heard of.

Lis - linear algebra library - was created in 2005.

Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.