+ y - U.I.U.C. Math
... It should be mentioned that certain cases of (5.2), adequate to establish the uniform convexity of Xp{Aff} for some (but not all) p and q, follow directly from Clarkson's inequalities without any convexity theorem. For example, if q§: 2, (5.4) becomes (1.2) for r = q, s = q'; hence (5.4) still holds ...
... It should be mentioned that certain cases of (5.2), adequate to establish the uniform convexity of Xp{Aff} for some (but not all) p and q, follow directly from Clarkson's inequalities without any convexity theorem. For example, if q§: 2, (5.4) becomes (1.2) for r = q, s = q'; hence (5.4) still holds ...
matrix
... • In other words, if At=[bij], then bij = aji for i=1,2,. . .,n and j = 1,2,. . .,m . ...
... • In other words, if At=[bij], then bij = aji for i=1,2,. . .,n and j = 1,2,. . .,m . ...
Introduction - SUST Repository
... association preserves distance in the sense that if a and b are two points of the plane , then the distance , d (Ta ,Tb ), between the points Ta and Tb equals the distance d (a,b) between the points a and b. Isometries are particularly important , because if a transformation preserves distance , the ...
... association preserves distance in the sense that if a and b are two points of the plane , then the distance , d (Ta ,Tb ), between the points Ta and Tb equals the distance d (a,b) between the points a and b. Isometries are particularly important , because if a transformation preserves distance , the ...
MM5 - CONTROL
... Compute angular and linear velocities and accelerations outward from {0}-{N} by iteration Compute forces and torques acting on each link Compute forces and torques from {N}-{0} by iteration ...
... Compute angular and linear velocities and accelerations outward from {0}-{N} by iteration Compute forces and torques acting on each link Compute forces and torques from {N}-{0} by iteration ...
2.1 Linear Equations and Problem Solving
... The solutions of an equation depend on the kinds of numbers being considered. For instance, in the set of rational numbers, x 2 10 has no solution because there is no rational number whose square is 10. However, in the set of real numbers the equation has the two solutions x 冪10 and x 冪10. A ...
... The solutions of an equation depend on the kinds of numbers being considered. For instance, in the set of rational numbers, x 2 10 has no solution because there is no rational number whose square is 10. However, in the set of real numbers the equation has the two solutions x 冪10 and x 冪10. A ...
Fast Fourier Transforms
... ⁶Tukey apparently studied the algorithm to help detect Soviet nuclear tests without actually visiting Soviet nuclear facilities, by interpolating off-shore seismic readings. Without his rediscovery, the nuclear test ban treaty would never have been ratified, and we’d all be speaking Russian, or more ...
... ⁶Tukey apparently studied the algorithm to help detect Soviet nuclear tests without actually visiting Soviet nuclear facilities, by interpolating off-shore seismic readings. Without his rediscovery, the nuclear test ban treaty would never have been ratified, and we’d all be speaking Russian, or more ...
Linear algebra
Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models.