scalaradj.n.

1656 T. Blount Glossographia Scalar, Scalary, leaning one way, ladderwise, not bolt up right.

1880 Linn. Soc. Jrnl. 15 92 Spire rather high, scalar.

1846 W. R. Hamilton in London, Edinb. & Dublin Philos. Mag. 3rd Ser. 29 26 The algebraically real part may receive, according to the question in which it occurs, all values contained on the one scale of progression of numbers from negative to positive infinity; we shall call it therefore the scalar part, or simply the scalar of the quaternion, and shall form its symbol by prefixing, to the symbol of the quaternion, the characteristic Scal., or simply S.

1853 Hamilton in London, Edinb. & Dublin Philos. Mag. 4th Ser. 5 322 The two values of the vector ρ, which answer to the two values of the scalar coefficient x.

1853 W. R. Hamilton Elem. Quaternions (1866) ii. i. 175 The Scalar (or Scalar Part) of a Quaternion.

1853 W. R. Hamilton Elem. Quaternions iii. iii. 721 The scalar equation of the polar of the latter point.

1873 J. C. Maxwell Treat. Electr. & Magnetism I. 9 Scalar quantities do not involve direction.

1911 Encycl. Brit. XXVII. 962/2 The mass of a body, the pressure of a gas, the charge of an electrified conductor, are instances of scalar magnitudes.

1932 R. Gans Vector Anal. ii. 58 Let W..be a scalar..property of a field, and let it be regarded as a function of the position and of the time.

1964 N. N. Hancock Matrix Anal. Electr. Machinery ii. 18 A ‘scalar’ matrix is a diagonal matrix in which all the elements on the principal diagonal are equal.

1928 G. Cooke Theory Mus. ii. 18 One cannot..over-emphasise the importance of these groups of notes in the theoretic study of scalar development.

1928 G. Cooke Theory Mus. vi. 77 The variety inherent in modulation and scalar variety.

1946 R. Blesh Shining Trumpets ii. 25 The basic material is recast in its scalar compass and its tonal intervals.

1959 M. T. Williams Art of Jazz (1960) xi. 106 Sliding tones peculiar to the scalar and harmonic structure.

1966 New Statesman 11 Feb. 204/1 The integration of triadic and scalar elements within a serial or non-tonal field.

1959 G. D. Mitchell Sociol. 130 Very often there is an identity of functional and scalar status.

1974 G. Leech Semantics ii. 21 A selection from indefinitely many possible scales, which in any case would only provide for associative meaning in so far as it is explicable in scalar terms.

1853 W. R. Hamilton Elem. Quaternions (1866) i. ii. 10 The..quotient..obtained by the division of two parallel vectors by another, including zero as a limit, may also be called a Scalar; because it can always be found..by the comparison of positions upon one common scale (or axis)... Such Scalars are..simply the Reals..of Algebra.

1853 W. R. Hamilton Elem. Quaternions (1866) i. ii. 11 The combination, ‘Scalar plus Vector,’ is a Quaternion.

1882 G. M. Minchin Uniplanar Kinematics 260 The result of the operation ∇² on any scalar is purely a scalar.

1903 Nature 22 Oct. 610/1 In Prof. Henrici's algebra the products of two vectors α, β are:—(αβ) a non-directional or ‘scalar’,..and [αβ] a vector perpendicular to the plane drawn through α and β.

1932 R. Gans Vector Anal. i. 2 We shall denote scalars by ordinary type and vectors by heavy type.

1965 E. M. Patterson & D. E. Rutherford Elem. Abstr. Algebra v. 145 By a scalar we shall mean an entity determined by a single real number and by a vector we shall mean an entity determined by both a positive real number, measuring magnitude, and a direction in space.

1932 R. Gans Vector Anal. i. 1 The field is called a scalar field or a vector field according as the quantity associated with the field is a scalar or a vector.

1959 M. R. Spiegel Schaum's Outl. Theory & Probl. Vector Anal. i. 3 The temperature at any point within or on the earth's surface at a certain time defines a scalar field.

1974 G. Reece tr. F. Hund Hist. Quantum Theory xv. 207 It was therefore a major advance when Pauli and Victor Weisskopf developed the quantum theory of a scalar field.

1956 A. A. Townsend Struct. Turbulent Shear Flow iii. 35 The double-correlation function depends only on a single scalar function.

1972 A. G. Howson Handbk. Terms Algebra & Anal. xxvi. 126 Functions such as f are often referred to as vector-valued functions and are denoted by symbols printed in bold type so as to distinguish them from real-valued or scalar functions.

1901 J. W. Gibbs & E. B. Wilson Vector Anal. i. 13 The laws which govern addition, subtraction, and scalar multiplication of vectors are identical with those governing these operations in ordinary scalar algebra.

1968 A. P. Armit Adv. Level Vectors ii. 25 (heading) Scalar multiplication of a vector..in terms of cartesian components.

1878 W. K. Clifford Elem. Dynamic 95 We are led to two different kinds of product of two vectors,..a vector product..and a scalar product.

1932 R. Gans Vector Anal. i. 17 By the scalar product of two vectors A and B we mean a scalar of magnitude equal to the product of the absolute values and the cosine of the angle between the vectors.

1941 G. Birkhoff & S. MacLane Surv. Mod. Algebra vii. 181 Physicists often speak of our inner product as a ‘scalar product’ of two vectors.

1968 E. T. Copson Metric Spaces ix. 139 In order to avoid confusion between multiplication of a vector by a scalar and the scalar product of two vectors, the scalar product of two vectors is often called their inner product.

1901 J. W. Gibbs & E. B. Wilson Vector Anal. ii. 68 The second triple product is the scalar product of two vectors, of which one is itself a vector product, as A · (B × C) or (A × B) · C. This sort of product has a scalar value and consequently is often called the scalar triple product.

1959 M. R. Spiegel Schaum's Outl. Theory & Probl. Vector Anal. ii. 17 The product A · (B × C) is sometimes called the scalar triple product or box product and may be denoted by [ABC].

1964 E. Œ. Wolstenhome Elem. Vectors ii. 38 If a, b, c are three vectors, any pair of them may be multiplied vectorially to form a new vector d, the third of the original vectors may then be multiplied by d, either scalarly to form what is known as a scalar triple product, or vectorially to form..the vector triple product.