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linear algebra[′lin·ē·ər ′al·jə·brə]
the part of algebra that is most important for applications. The theory of linear equations was the first problem to arise that pertained to linear algebra. The development of the theory led to the creation of the theory of determinants and subsequently to the theory of matrices and the related theories of vector spaces and linear transformations in them. Linear algebra also encompasses the theory of forms, in particular quadratic forms, and, in part, the theory of invariants and the tensor calculus. Some branches of functional analysis constitute a further development of corresponding problems of linear algebra associated with the passage from n-dimensional vector spaces to infinite-dimensional linear spaces.
REFERENCESAleksandrov, P. S. Lektsii po analiticheskoi geometrii .... Moscow, 1968.
Kurosh, A. G. Kurs vysshei algebry, 9th ed. Moscow, 1968.
Mal’tsev, A. I. Osnovy lineinoi algebry, 3rd ed. Moscow, 1970.
Faddeev, D. K., and V. N. Faddeeva. Vychislitel’nye metody lineinoi algebry, 2nd ed. Moscow-Leningrad, 1963.