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Is linear algebra the same as matrix algebra?

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What you call matrix algebra is actually the properties on linear maps on finite dimension vector spaces. Linear algebra, in its most general definition, deals both with finite and infinite dimensions. For instance, solving the equation system x+2y=0. And 2x+3y=0. read more

Linear algebra, in its most general definition, deals both with finite and infinite dimensions. For instance, solving the equation system x+2y=0 And 2x+3y=0 Is a finite dimension (two dimensional since we have two variables) linear algebra problem, so it can be represented with matrices. read more

Matrix theory is the specialization of linear algebra to the case of finite dimensional vector spaces and doing explicit manipulations after fixing a basis. More precisely: The algebra of $n \times n$ matrices with coefficients in a field $F$ is isomorphic to the algebra of $F$-linear homomorphisms from an $n$-dimensional vector space $V$ over $F$, to itself. read more

Algebra itself is the study and determination of unknowns. There are many types of unknowns, and many ways to study them, hence the many varieties of algebra. “Regular” algebra is the study of normal, everyday “real” numbers. Linear algebra is the study of matrices. Etc. read more

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