document.write( "Question 1172394: If U and V are subspaces of a 7 dimensional vector space V, then what is the possible dimension of the intersection of U and V? \n" ); document.write( "

Algebra.Com's Answer #797421 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "If U and V are subspaces of a 7 dimensional vector space V, then what is the possible dimension of the intersection of U and V?
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\n" ); document.write( "\n" ); document.write( "As I see from your post, you use the letter V for both the space and subspace.\r
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What is it: an error or a mistake ? Or BOTH ?

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\n" ); document.write( "\n" ); document.write( "Comment from student: Vector space is X and U and V are subspaces of X.\r
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\n" ); document.write( "\n" ); document.write( "My response : \r
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document.write( "    Let  n be the dimension of subspace U,  n = dim(U);\r\n" );
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document.write( "    Let  m be the dimension of subspace V,  m = dim(V).\r\n" );
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document.write( "    Let  W be intersection of the linear subspaces U and V.\r\n" );
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document.write( "    Then W itself is the linear subspace, and its dimension d(W) can be any integer non-negative number\r\n" );
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document.write( "        d(W) <= min ( d(U), d(W) ).\r\n" );
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document.write( "    That is all what I can say/answer in response to the posed question.\r\n" );
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