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अंग्रेजी-हिंदी > outer product उदाहरण वाक्य

outer product उदाहरण वाक्य

उदाहरण वाक्य
41.If " V " and " W " are finite-dimensional, then the space of all linear transformations from " W " to " V ", denoted, is generated by such outer products; in fact, the rank of a matrix is the minimal number of such outer products needed to express it as a sum ( this is the "'tensor rank "'of a matrix ).

42.If " V " and " W " are finite-dimensional, then the space of all linear transformations from " W " to " V ", denoted, is generated by such outer products; in fact, the rank of a matrix is the minimal number of such outer products needed to express it as a sum ( this is the "'tensor rank "'of a matrix ).

43.More abstractly, the outer product is the bilinear map W \ times V ^ * \ to \ operatorname { Hom } ( V, W ) sending a vector and a covector to a rank 1 linear transformation ( simple tensor of type ( 1, 1 ) ), while the inner product is the bilinear evaluation map V ^ * \ times V \ to F given by evaluating a covector on a vector; the order of the domain vector spaces here reflects the covector / vector distinction.

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