notes
... As we have seen, the basic matrix multiply outlined in the previous section will usually be at least an order of magnitude slower than a well-tuned matrix multiplication routine. There are several reasons for this lack of performance, but one of the most important is that the basic algorithm makes p ...
... As we have seen, the basic matrix multiply outlined in the previous section will usually be at least an order of magnitude slower than a well-tuned matrix multiplication routine. There are several reasons for this lack of performance, but one of the most important is that the basic algorithm makes p ...
Garrett 03-30-2012 1 • Interlude: Calculus on spheres: invariant integrals, invariant
... vector subspace W of V stable under the action of G... and when V is infinite-dimensional W must be topologically closed. A representation V of G is irreducible if there is no proper Gsubrepresentation, that is, if there is no G-subrepresentation of V other than {0} and V itself. A G-homomorphism fr ...
... vector subspace W of V stable under the action of G... and when V is infinite-dimensional W must be topologically closed. A representation V of G is irreducible if there is no proper Gsubrepresentation, that is, if there is no G-subrepresentation of V other than {0} and V itself. A G-homomorphism fr ...
8.1 General Linear Transformation
... If V is a finite-dimensional vector space and T:V ->V is a linear operator then the following are equivalent. (a)T is one to one (b) ker(T) = {0} (c)nullity(T) = 0 (d)The range of T is V;that is ,R(T) =V ...
... If V is a finite-dimensional vector space and T:V ->V is a linear operator then the following are equivalent. (a)T is one to one (b) ker(T) = {0} (c)nullity(T) = 0 (d)The range of T is V;that is ,R(T) =V ...
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Document
... Normal and Tangential force If the particle’s accelerated motion is not completely specified, then information regarding the directions or magnitudes of the forces acting on the particle must be known or computed. Now, consider the case in which the force P causes the particle to move along the pat ...
... Normal and Tangential force If the particle’s accelerated motion is not completely specified, then information regarding the directions or magnitudes of the forces acting on the particle must be known or computed. Now, consider the case in which the force P causes the particle to move along the pat ...
Tensors - University of Miami Physics Department
... apparatus for computation in an arbitrary basis, but for the moment it’s a little simpler to start out with the more common orthonormal basis vectors, and even there I’ll stay with rectangular coordinates for a while. (Recall that an orthonormal basis is an independent set of orthogonal unit vectors ...
... apparatus for computation in an arbitrary basis, but for the moment it’s a little simpler to start out with the more common orthonormal basis vectors, and even there I’ll stay with rectangular coordinates for a while. (Recall that an orthonormal basis is an independent set of orthogonal unit vectors ...
Numbers and Vector spaces
... There exists an element 1 6= 0 in F such that 1 · x = x for every x in F. For every x 6= 0 in F there exists y in F such that xy = 1. This y is called x−1 . These are the properties of multiplication. Now the properties relating addition and multiplication: x(y + z) = zy + xz. This are all properti ...
... There exists an element 1 6= 0 in F such that 1 · x = x for every x in F. For every x 6= 0 in F there exists y in F such that xy = 1. This y is called x−1 . These are the properties of multiplication. Now the properties relating addition and multiplication: x(y + z) = zy + xz. This are all properti ...