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Date: 6-6-2021
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Suppose that and . Then the quotient space (read as " mod ") is isomorphic to .
In general, when is a subspace of a vector space , the quotient space is the set of equivalence classes where if . By " is equivalent to modulo ," it is meant that for some in , and is another way to say . In particular, the elements of represent . Sometimes the equivalence classes are written as cosets .
The quotient space is an abstract vector space, not necessarily isomorphic to a subspace of . However, if has an inner product, then is isomorphic to
In the example above, .
Unfortunately, a different choice of inner product can change . Also, in the infinite-dimensional case, it is necessary for to be a closed subspace to realize the isomorphism between and , as well as to ensure the quotient space is a T2-space.
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علامات بسيطة في جسدك قد تنذر بمرض "قاتل"
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أول صور ثلاثية الأبعاد للغدة الزعترية البشرية
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مدرسة دار العلم.. صرح علميّ متميز في كربلاء لنشر علوم أهل البيت (عليهم السلام)
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