document.write( "Question 1161624: What are the four main things we need to define for a vector space? \n" ); document.write( "
Algebra.Com's Answer #787004 by solver91311(24713)![]() ![]() You can put this solution on YOUR website! \r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "1. A set of vectors over a field\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "2. The operation of vector addition and the set of vectors is closed over this operation. That is, if you add one vector to another, you get a vector that is in the same set.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "3. The operation of scalar multiplication and the set of vectors is closed over this operation. If you multiply a field element by a vector element you get a vector in the set of vectors.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "4. The operations adhere to the following axioms:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Associativity for addition, Commutativity for addition, an Identity Element for addition exists, an Inverse Element for addition exists, Compatibility of scalar and field multiplication [ab(v) = a(bv)], an Identity Element for scalar multiplication exists, Distributivity of scalar multiplication over vector addition, Distributivity of scalar multiplication wrt field addition.\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "John \n" ); document.write( " \n" ); document.write( "My calculator said it, I believe it, that settles it \n" ); document.write( " ![]() \n" ); document.write( " |