Homework 3
... is the dot product uti uj for i 6= j? Let’s assume for the moment that n ≤ m. This implies that there must exist a unit vector w that is orthogonal to all u1 , · · · , un . What is Aw? E. Finally, let U = [v1 v2 · · · vn ], V = [u1 u2 · · · un ] and Σ the diagonal matrix with diagonal entries γ1 , γ ...
... is the dot product uti uj for i 6= j? Let’s assume for the moment that n ≤ m. This implies that there must exist a unit vector w that is orthogonal to all u1 , · · · , un . What is Aw? E. Finally, let U = [v1 v2 · · · vn ], V = [u1 u2 · · · un ] and Σ the diagonal matrix with diagonal entries γ1 , γ ...
Abstract Vector Spaces and Subspaces
... 1. S, the set of all doubly infinite sequences, with addition and scalar multiplication defined element-wise 2. Pn , the set of all polynomials with real coefficients of degree at most n, with addition and scalar multiplication being the usual addition and constant multiple of functions 3. the set o ...
... 1. S, the set of all doubly infinite sequences, with addition and scalar multiplication defined element-wise 2. Pn , the set of all polynomials with real coefficients of degree at most n, with addition and scalar multiplication being the usual addition and constant multiple of functions 3. the set o ...
Homework 6
... Homework is assigned on Fridays; it is due at the start of class the week after it is assigned. So this homework is due May 17th. Problem 1. Give an example of a Riemannian metric on a sphere containing a non-periodic infinite geodesic which is not dense (i.e. its closure is not the entire sphere). ...
... Homework is assigned on Fridays; it is due at the start of class the week after it is assigned. So this homework is due May 17th. Problem 1. Give an example of a Riemannian metric on a sphere containing a non-periodic infinite geodesic which is not dense (i.e. its closure is not the entire sphere). ...
