 | David G. Luenberger - 1997 - 348 sivua
...generalization of a result for parallelograms in twodimensional geometry. The sum of the squares of the lengths of the diagonals of a parallelogram is equal to twice the sum of the squares of two adjacent sides. See Figure 3.1. Since a pre-Hilbert space is a special kind of normed linear space,... | |
 | Andrew M. Bruckner, Judith B. Bruckner, Brian S. Thomson - 1997 - 683 sivua
...• The next theorem is usually called the parallelogram law because of its geometric interpretation: the sum of the squares of the diagonals of a parallelogram is the sum of the squares of the sides. This characterizes the norm in a Hilbert space. If a normed linear... | |
 | Geoffrey C. Smith - 2000 - 236 sivua
...two ways, (b) Replace 6 by —6 in part (a), and add this equation to the old part (a) equation, (c) The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the four sides of the parallelogram. 3.7 (a) m = a2 + 6 and n = c2 + d2 for... | |
 | Lorenzo Farina, Sergio Rinaldi - 2000 - 324 sivua
...also possible to extend to pre-Hilbert spaces the well-known "parallelogram law", which states that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the sides. Indeed, it is easy to verify that ll* + y||2 + ||*-yf = 2|N|2+2||y||2.... | |
 | Fred Szabo - 2000 - 682 sivua
...norms. The law takes its name from ordinary geometry, where it says that the sum of the squares on the diagonals of a parallelogram is equal to twice the sum of the squares on its sides. THEOREM 7.7 (Parallelogram law) If ||z|| is an inner product norm on a real vector space... | |
 | Lokenath Debnath - 2002 - 586 sivua
...called the parallelogram law because of its remarkable geometric interpretation, which reveals that the sum of the squares of the diagonals of a parallelogram is the sum of the squares of the sides. This characterizes the norm in a Hilbert space. Theorem 2.6.2... | |
 | Abul Hasan Siddiqi - 2003 - 614 sivua
...Characterization of Hilbert Space From the elementary geometry {geometry of the plane), we know that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides. The following result gives a generalization of this result to... | |
 | J. J. Duistermaat, J. A. C. Kolk - 2004 - 444 sivua
...(iv) deduce (L П Л/)1 = L1 + Л/1. Exercise 1.2 (Parallelogram identity). Verify, for x and ye R", That is, the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of the sides. Exercise 1.3 (Symmetry identity - needed for Exercise 7.70).... | |
 | N. P. Bali, N. Ch. Narayana Iyengar - 2004 - 1438 sivua
...Prove that the median to the base of an isosceles triangle is perpendicular to the base. 11. Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares on its four sides. 12. Prove that in a tetrahedron, if two pairs of opposite... | |
 | Jamal T. Manassah - 2006 - 486 sivua
...Dirac notation, generalize to n-dimensions the 2-D geometry Parallelogram theorem, which states that the sum of the squares of the diagonals of a parallelogram is equal to twice the sum of the squares of the side; or that ||u + zf +||5-5||2 =2||u|2+2||i;||2 Pb. 7.6 Referring to the inequality of Eq. (7.43),... | |
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The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its four Dem.— Let ABCD be the a. 
