Cross Product Of Two Vectors Is Not Commutative

Let K be a field and let A be a vector space over K equipped with an additional binary operation from A A to A denoted here by ie. In mathematics the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas volumes and their higher-dimensional analoguesThe exterior product of two vectors and denoted by is called a bivector and lives in a space called the exterior square a vector space that is distinct from the original space of vectors.

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If x and y are any two elements of A x y is the product of x and yThen A is an algebra over K if the following identities hold for all elements x y z A and all elements often called scalars a and b of K.

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