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A scalar is a one-component quantity that is invariant under rotations of the coordinate system.

The scalar triple product of three vectors A, B, and C is denoted [A,B,C] and defined by [A,B,C] = A·(BxC) (1) = B·(CxA) (2) = C·(AxB) (3) = det(ABC) (4) = |A_1 A_2 A_3; B_1 ...

The term "product" refers to the result of one or more multiplications. For example, the mathematical statement a×b=c would be read "a times b equals c," where a is called ...

A map f:R^n|->R which assigns each x a scalar function f(x).

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...

A diagonal matrix whose diagonal elements all contain the same scalar lambda. A scalar matrix is therefore equivalent to lambdaI, where I is the identity matrix.

Scalar multiplication refers to the multiplication of a vector by a constant s, producing a vector in the same (for s>0) or opposite (for s<0) direction but of different ...

The scalar curvature, also called the "curvature scalar" (e.g., Weinberg 1972, p. 135; Misner et al. 1973, p. 222) or "Ricci scalar," is given by R=g^(mukappa)R_(mukappa), ...

A conservative vector field (for which the curl del xF=0) may be assigned a scalar potential where int_CF·ds is a line integral.

Let A, B, and C be three polar vectors, and define V_(ijk) = |A_i B_i C_i; A_j B_j C_j; A_k B_k C_k| (1) = det[A B C], (2) where det is the determinant. The V_(ijk) is a ...