External Composition : LInear Algebra : Degree

 External Composition : 

       An external composition means it is a binary operation performed between two different kinds of elements.

  For example : 

   In the definition of vector space, The scalar multiplication condition is an external composition because

 the scalar multiplication condition is  

               for a, 𝞊 F and 𝜶 𝞊  V ⇒  a𝜶 𝞊  V

    In this condition the product a𝜶 performed between a scalar a and a vector 𝜶

                                         ***

* The fourth dimensional objects

* what is a dimension of an object? 

* The Euclidean space  ℛ n

* Historical Introduction to Linear Algebra

  * Theorem on vector space  

*  Let V(F) be a vector space and let W ⊆ V. The necessary and sufficient conditions for W 

 to be a subspace of V are (i) 𝜶 𝞊 W, 𝞫 𝞊 W ⇒  𝜶 - 𝞫 𝞊 W   (ii) a 𝞊 F , 𝜶 𝞊 W ⇒ a𝜶 𝞊 W.

































































#vector #algebra #vector algebra   #iit #jee #mains #dimension #basis

            

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