The vector spaces relevant to quantum mechanics, first the real numbers To go from the familiar three-dimensional vector space to Vector space does not include that the vectors have a magnitude-that wouldīe an additional requirement, giving what is called a normed vector space. Notice that the list of necessary properties for a general The operators are, however, restricted to being Multiplication by a number are generalized to more abstract operations between Three-dimensional real vectors, but the operations of addition and Space: a general vector space has the properties we’ve listed above for Mathematicians have generalized the definition of a vector Null vector ( 0, 0, 0 ) and each vector has an additive inverse ( − v 1, − v 2, − v 3 ) which added to the original vector gives the
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