Module 5 Revision Check
... Draw lines, angles, triangles and other 2-D shapes; construct cubes, regular tetrahedral, square-based pyramids and other 3-D shapes Use straight edge and compasses to do standard constructions including equilateral triangle with a given side, the midpoint and perpendicular bisector of a line segmen ...
... Draw lines, angles, triangles and other 2-D shapes; construct cubes, regular tetrahedral, square-based pyramids and other 3-D shapes Use straight edge and compasses to do standard constructions including equilateral triangle with a given side, the midpoint and perpendicular bisector of a line segmen ...
Chemistry 431 - NC State University
... Using these principles we can see that σv’ has a character of +1. The identity always has a character equal to the number of basis functions. Here E = 9. Using the character of the 4 symmetry operations of the C2v point group we can construct a representation Γ. ...
... Using these principles we can see that σv’ has a character of +1. The identity always has a character equal to the number of basis functions. Here E = 9. Using the character of the 4 symmetry operations of the C2v point group we can construct a representation Γ. ...
Conformational Space
... SVD of rxN matrix, where N > r, takes O(r2N) time Here r ~ (n/m)2 So, time complexity is O(n4N) Would be too costly without m-averaging ...
... SVD of rxN matrix, where N > r, takes O(r2N) time Here r ~ (n/m)2 So, time complexity is O(n4N) Would be too costly without m-averaging ...
Matrices
... 5. For any square matrix A show that A At is symmetric and A At is skew-symmetric. 6. Let A be an idempotent matrix. Show that I-A is also idempotent. 7. A square matrix A is said to commute with a matrix B iff AB=BA. When does a 3 3 matrix A commute with the matrix Ers ? 8. Show that if a 3 ...
... 5. For any square matrix A show that A At is symmetric and A At is skew-symmetric. 6. Let A be an idempotent matrix. Show that I-A is also idempotent. 7. A square matrix A is said to commute with a matrix B iff AB=BA. When does a 3 3 matrix A commute with the matrix Ers ? 8. Show that if a 3 ...
Notes
... kyk kxk The quantity κ(A) = kAkkA−1 k is the condition number for matrix multiplication. It is also the condition number for multiplication by the inverse (solving a linear system). Ill-conditioned matrices are “close to” singular in a well-defined sense: if κ(A) 1, then there is a perturbation E, ...
... kyk kxk The quantity κ(A) = kAkkA−1 k is the condition number for matrix multiplication. It is also the condition number for multiplication by the inverse (solving a linear system). Ill-conditioned matrices are “close to” singular in a well-defined sense: if κ(A) 1, then there is a perturbation E, ...
