| 单词 | linear algebra |
| 释义 | > as lemmaslinear algebra linear algebra n. Mathematics a finite-dimensional vector space, with multiplication defined and distributive over addition, in which (λa)b = λ(ab) = a(λb) for any scalar λ of the associated field and any vectors a and b; also, the branch of algebra which deals with the properties of these entities, esp. of vector spaces over the real or complex numbers. ΘΚΠ the world > relative properties > number > algebra > [noun] > branch or subset of quadratic1674 tactic1861 linear algebra1870 group theory1888 subalgebra1903 Clifford algebra1907 the world > relative properties > number > mathematical number or quantity > tensor > [noun] > vector > vector space linear algebra1870 Lie algebra1935 vector space1937 1870 B. Peirce in Amer. Jrnl. Math. (1881) 4 107 An algebra in which every expression is reducible to the form of an algebraic sum of terms, each of which consists of a single letter with a quantitative coefficient, is called a linear algebra. 1945 E. T. Bell Devel. Math. (ed. 2) x. 231 The introduction of general methods into linear algebra, beginning in the first decade of the twentieth century, prepared that vast field of mathematics..for partial arithmetization in the second and third decades. 1965 E. M. Patterson & D. E. Rutherford Elem. Abstr. Algebra v. 187 The set of all m × m matrices over a field F forms a linear algebra of dimension m2. 1975 I. Stewart Concepts Mod. Math. xv. 227 A proper understanding of linear algebra requires a synthesis of three points of view: (i) the underlying geometrical motivation, (ii) the abstract algebraic formulation, (iii) the matrix-theoretic technique. 1986 C. W. Norman Undergraduate Algebra p. vii Many of the problems which linear algebra sets out to solve are dealt with in a practical way by the row-reduction algorithm in Chapter 8. < as lemmas |
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