Noun
a real number (a scalar) that is the product of two vectors
Source: WordNetClifford simplified the quaternion study by isolating the dot product and cross product of two vectors from the complete quaternion product. Source: Internet
If m is in the same direction as B then the dot product is positive and the gradient points 'uphill' pulling the magnet into regions of higher B -field (more strictly larger m · B ). Source: Internet
For the real case this corresponds to the dot product of the results of directionally different scaling of the two vectors, with positive scale factors and orthogonal directions of scaling. Source: Internet
In a geometric algebra for which the square of any nonzero vector is positive, the inner product of two vectors can be identified with the dot product of standard vector algebra. Source: Internet
In those disciplines we would write the product as (the bra–ket notation of quantum mechanics ), respectively (dot product as a case of the convention of forming the matrix product AB as the dot products of rows of A with columns of B ). Source: Internet
More precisely, when H is differentiable, the dot product of the gradient of H with a given unit vector is equal to the directional derivative of H in the direction of that unit vector. Source: Internet