Results 271 to 280 of about 289,909 (310)
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1995
Real and complex inner product spaces are defined and several examples are studied. Elementary properties of inner products, such as the Cauchy–Schwarz–Bunyakovsky Theorem and Minkowski’s inequality are proven. The Lagrange identity relating inner and cross products in three-dimensional real vector spaces is proven.
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Real and complex inner product spaces are defined and several examples are studied. Elementary properties of inner products, such as the Cauchy–Schwarz–Bunyakovsky Theorem and Minkowski’s inequality are proven. The Lagrange identity relating inner and cross products in three-dimensional real vector spaces is proven.
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1978
So far in our study of vector spaces and linear transformations we have made no use of the notions of length and angle, although these concepts play an important role in our intuition for the vector algebra of ℝ2 and ℝ3. In fact the length of a vector and the angle between two vectors play very important parts in the further development of linear ...
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So far in our study of vector spaces and linear transformations we have made no use of the notions of length and angle, although these concepts play an important role in our intuition for the vector algebra of ℝ2 and ℝ3. In fact the length of a vector and the angle between two vectors play very important parts in the further development of linear ...
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Comments on "Inner Product Computers"
IEEE Transactions on Computers, 1979The results for different hardware configurations of inner product computers presented by Swartzlander et al.1 are in error. In their Table I, the pipelined quasi-serial processor is credited with the ability to evaluate a complete inner product in 10 ns. The clock rate may be 10 ns but several clocks are required to evaluate one inner product.
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Appollonius and Inner Products
The American Mathematical Monthly, 1974Desmond Fearnley-Sander, J. S. V. Symons
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Interesting inner-product scans
Proceedings of the 2003 conference on APL: stretching the mind, 2003The inner-product scan allows a straight-forward calculation of interest-bearing accounts or annuities without a loop in APL. It allows arbitrary deposit (or withdrawal) and interest each period. A defined scan operator for associative functions is provided to improve performance by avoiding the repeated reductions of increasingly long vectors that ...
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On a Characterisation of Inner Product Spaces
gmj, 2001Abstract It is well known that for the Hilbert space H the minimum value of the functional F μ (f) = ∫ H ‖f – g‖2 dμ(g), f ∈ H, is achived at the mean of μ for any probability measure μ with strong second moment on H.
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Applications of the inner product computer
Proceedings of the annual conference on - ACM'73, 1973Recently much interest has been expressed in the idea that future improvements in computer speed will be due primarily to architectural innovations as opposed to improvement in the characteristics of components (i.e., logic circuits, delays, memories, cycle times, etc.).
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International Journal of Electrical Power and Energy Systems, 2022
Xiaowei Wang, Zhenfeng Liang, Jie Gao
exaly
Xiaowei Wang, Zhenfeng Liang, Jie Gao
exaly