Abstract
Some relevant mathematical results are collected in this chapter. These results find a wide application within the realm of analysis, synthesis and optimization of mechanisms. Often, rigorous proofs are not provided; however a reference list is given at the end of the chapter, where the interested reader can find the required details.
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References
Lang S., Linear Algebra, Addison-Wesley Publishing Co., Menlo Park, 1970, pp. 39 and 40.
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Finkbeiner, D.F., Matrices and Linear Transformations, W.H. Freeman and Company, San Francisco, 1960, pp. 139–142
Halmos, P.R., Finite-Dimensional Vector Spaces, Springer-Verlag, N. York, 1974.
Businger P. and G.H. Golub, “Linear Least Squares Solutions by Householder Transformations”, in Wilkinson J.H. and C. Reinsch, eds., Handbook for Automatic Computation, Vol. II, Springer-Verlag, N. York, 1971, pp. 111–118
Stewart, G.W., Introduction to Matrix Computations, Academic Press, N.York, 1973, pp. 208–249.
Soderstrom T. and G.W. Stewart, “On the numerical properties of an iterative method for computing the Moore-Penrose generalized inverse”, SIAM J. on Numerical Analysis, Vol. II, No. 1, March 1974.
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Moler C.B., Matrix Eigenvalue and Least Square Computations,Computer Science Departament, Stanford University, Stanford, California, 1973 pp. 4. 1–4. 15
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Angeles, J., “Optimal synthesis of linkages using Householder reflections”, Proceedings of the Fifth World Congress on the Theory of Machines and Mechanisms, vol. I, Montreal, Canada, July 8–13, 1979, pp. 111’-114.
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© 1982 Springer-Verlag Berlin, Heidelberg
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Angeles, J. (1982). Mathematical Preliminaries. In: Spatial Kinematic Chains. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48819-1_1
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DOI: https://doi.org/10.1007/978-3-642-48819-1_1
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