

Matrix Size & Validation
Vector Algebra What is Vector? Vector Norm Unit Vector Vector Addition Vector Subtraction Vector Scalar Multiple Vector Multiplication Vector Inner Product Vector Outer Product Vector Cross Product Vector Triple Cross Product Vector Triple Dot Product Scalar Triple Product Orthogonal & Orthonormal Vector Cos Angle of Vectors Scalar and Vector Projection Matrix Algebra What is a matrix? Special Matrices Matrix One Null Matrix Matrix Diagonal Is Diagonal Matrix? Identity Matrix Matrix Determinant Matrix Sum Matrix Trace Matrix Basic Operation Is Equal Matrix? Matrix Transpose Matrix Addition Matrix Subtraction Matrix Multiplication Matrix Scalar Multiple Hadamard Product Horizontal Concatenation Vertical Concatenation Elementary Row Operations Matrix RREF Finding inverse using RREF (GaussJordan) Finding Matrix Rank using RREF Matrix Inverse Is Singular Matrix? Linear Transformation Matrix Generalized Inverse Solving System of Linear Equations Linear combination, Span & Basis Vector Linearly Dependent & Linearly Independent Change of basis Matrix Rank Matrix Range Matrix Nullity & Null Space Eigen System Matrix Eigen Value & Eigen Vector Symmetric Matrix Matrix Eigen Value & Eigen Vector for Symmetric Matrix Similarity Transformation and Matrix Diagonalization Matrix Power Orthogonal Matrix Spectral Decomposition Singular Value Decomposition Resources on Linear Algebra 
Cross Product Vector cross product is also called vector product because the result of the vector multiplication is a vector. It can only be performed for two vectors of the same size. Geometrically, when you have two vectors on a plane, the cross product will produce another vector perpendicular to the plane span by the two input vectors. The direction of the cross product vector is following the direction of the thumb finger in your right hand when the four other fingers indicate the angle from the first vector to the second vector, as shown in the following figures.
Computation of cross productFor 1 or two dimensional vector, the cross product produces zero vectors because they do not make a plane yet. Starting from 3 dimensions, the cross product can be computed algebraically using simple arrangement and a simple rule below The arrangement to compute vector cross product Simple rule to compute cross productAfter the arrangement above, multiply the elements of the vectors in diagonal direction and then minus with the product of elements in counter diagonal direction Unit vector represent the first, second and third position of vector elements. Thus, here is the final result Example For higher dimension, we use the same rule but programmatically, it is easier if we use a formula Input: vector a, vector b both have equal length The interactive program of cross product below shows the cross product of two vectors of the same dimension. The program will also show you the internal computation so that you can check your own manual computation. If you click “Random Example” button, the program will generate random input vectors in the right format. In the applications, cross product is useful for constructing coordinate system mostly in 3dimensional space. PropertiesSome important properties of vector cross product are
See also: triple dot product, triple cross product, scalar triple product, inner product Rate this tutorial or give your comments about this tutorial Preferable reference for this tutorial is Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\ tutorial\LinearAlgebra\ 



