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For each vector u 2 V, the norm (also called the length) of u is deflned as the number kuk= p hu;ui If kuk = 1, we call u a unit vector and u is said to be normalized For any nonzero vector v 2 V, we have the unit vector v^ = 1 kvk v This process is called normalizing v Let B = u1;u2;;un be a basis of an ndimensional inner product space VFor vectors u;v 2 V, write. J ^ O ̃y W >FSUP i t b g E H ^ @ X ^ h A b v p h { h j > EC4 iSUP iTrekker 12 f6 C4 i V t H j C t ^ u @SUP iSUP iTrekker 12 f6 i A C T b v A C g b J 12 f6 j. 22 Example Rm×nSuppose A = (a ij) and B = (b ij) are matrices in Rm×nThe usual inner product on Rm×n is given by hA,Bi = Xm i=1 j=1 a ijb ij Note that this is the sum of the pointwise products of the elements of A and B.
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The formula for change provides a model to assess the relative strengths affecting the likely success of organisational change programs The formula was created by David Gleicher while he was working at Arthur D Little in the early 1960s, and refined by Kathie Dannemiller in the 1980s. J ^ O ̃y W >FSUP i t b g E H ^ @ X ^ h A b v p h { h j > E ^ C _ X g @ t B b V n ^ 106. Real Analysis Homework #1 Yingwei Wang ∗ Department of Mathematics, Purdue University, West Lafayette, IN, USA 1 Banach space Question Let (xn) ⊂ X be a Banach space, and P∞ n=1 kxnk is convergentProof that.
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