Lecture 16 notes. - Cs.princeton.edu
... two still leaves infinite sets. For this we use the notion of the containing Ellipsoid of a convex body. An axis aligned ellipsoid is the set of all x such that n X x2 i ...
... two still leaves infinite sets. For this we use the notion of the containing Ellipsoid of a convex body. An axis aligned ellipsoid is the set of all x such that n X x2 i ...
ENGR-25_Lec-21_Linear_Equations-2
... The left-division method will give a solution with some of the unknowns arbitrarily set equal to zero, but this solution is NOT the general solution; it’s just ONE solution (of Trillions) An infinite number of solutions might exist even when the number of equations equals the number of unknowns. The ...
... The left-division method will give a solution with some of the unknowns arbitrarily set equal to zero, but this solution is NOT the general solution; it’s just ONE solution (of Trillions) An infinite number of solutions might exist even when the number of equations equals the number of unknowns. The ...
Document
... pf: 」Suppose T is one-to-one. Then T(v) = 0 can have only one solution: v = 0. In this case, ker(T) = {0}. 」Suppose ker(T) = {0} and T(u) = T(v). Because T is a linear transformation, it follows that T(u – v) = T(u) – T(v) = 0 This implies that u – v lies in the kernel of T and must therefore equa ...
... pf: 」Suppose T is one-to-one. Then T(v) = 0 can have only one solution: v = 0. In this case, ker(T) = {0}. 」Suppose ker(T) = {0} and T(u) = T(v). Because T is a linear transformation, it follows that T(u – v) = T(u) – T(v) = 0 This implies that u – v lies in the kernel of T and must therefore equa ...
Rotation Matrices 2
... in the original coordinate system. This means that the combined rotation matrix RpointsXYZ = RpointsZRpointsYRpointsX, for example, represents rotation about proximal X, then proximal Y, then proximal Z. That’s not what we want. We want to rotate about X (which is the same for proximal and distal se ...
... in the original coordinate system. This means that the combined rotation matrix RpointsXYZ = RpointsZRpointsYRpointsX, for example, represents rotation about proximal X, then proximal Y, then proximal Z. That’s not what we want. We want to rotate about X (which is the same for proximal and distal se ...
