Cross products {matrix cross product} of two square matrices indicate interactions between set-A and set-B members: A x B. Matrix cross products can find extensive quantities, such as area, from intensive quantities, such as vector distances. Matrix cross products are differences between matrix dot product and reverse matrix dot product: A x B = (A . B) - (B . A). Only square matrices can have matrix cross products. Matrix cross products find square matrices. For 1x1 matrices [a11] and [b11], matrix cross product is [a11*b11 - b11*a11] = [0]. For 2x2 matrices [a11 a12 / a21 a22] and [b11 b12 / b21 b22], matrix cross product is [a11*b11 + a11*b21 a12*b12 + a12*b22 / a21*b11 + a21*b21 a22*b12 + a22*b22] - [b11*a11 + b11*a21 b12*a12 + b12*a22 / b21*a11 + b21*a21 b22*a12 + b22*a22] = [a11*b11 + a11*b21 - b11*a11 - b11*a21 a12*b12 + a12*b22 - b12*a12 - b12*a22 / a21*b11 + a21*b21 - b21*a11 - b21*a21 a22*b12 + a22*b22 - b22*a12 - b22*a22] = [a11*b21 - b11*a21 a12*b22 - b12*a22 / a21*b11 - b21*a11 a22*b12 - b22*a12]. If both matrices are the same, matrix cross product is zero matrix: A x A = 0. Matrix cross products are not commutative: A x B = (A . B) - (B . A) <> (B . A) - (A . B) = B x A.
Mathematical Sciences>Algebra>Equation>System>Matrix>Operations
3-Algebra-Equation-System-Matrix-Operations
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0224