Math for Programmers
... • If at least one Aii (diagonal from upper left to lower right) are non-zero and all others are zero, is diagonal matrix ...
... • If at least one Aii (diagonal from upper left to lower right) are non-zero and all others are zero, is diagonal matrix ...
Invariant of the hypergeometric group associated to the quantum
... a suitable set of pseudo-reflexions generators Rj like (2.9), (2.10), up to constant multiplication on Qj , so that they determine the quadratic invariant Gram matrix like (2.11). proof The proposition 2.7 implies that every generator Ti is a product of pseudo-reflexions Mj with sjk possibly differe ...
... a suitable set of pseudo-reflexions generators Rj like (2.9), (2.10), up to constant multiplication on Qj , so that they determine the quadratic invariant Gram matrix like (2.11). proof The proposition 2.7 implies that every generator Ti is a product of pseudo-reflexions Mj with sjk possibly differe ...
Tutorial 5
... 2. Redo the question, only this time you may not use recursion. ;; (square x) returns the square of x ;; Args: x - a number, the square if which is returned ;; Pre: x is a number ;; Post: none ;; Return: the square of x (define (square x) (* x x)) ;; (norm lst) returns a Euclidean norm of a vector, ...
... 2. Redo the question, only this time you may not use recursion. ;; (square x) returns the square of x ;; Args: x - a number, the square if which is returned ;; Pre: x is a number ;; Post: none ;; Return: the square of x (define (square x) (* x x)) ;; (norm lst) returns a Euclidean norm of a vector, ...
Principles of Scientific Computing Linear Algebra II, Algorithms
... primes. Note that M1 A has lost the symmetry of A. We can restore this symmetry by multiplying from the right by M1∗ This has the effect of subtracting a1i a11 times the first column of M1 A from column i for i = 2, . . . , n. Since the top row of A has not changed, this has the effect of setting th ...
... primes. Note that M1 A has lost the symmetry of A. We can restore this symmetry by multiplying from the right by M1∗ This has the effect of subtracting a1i a11 times the first column of M1 A from column i for i = 2, . . . , n. Since the top row of A has not changed, this has the effect of setting th ...
Solutions to HW 5
... Remark 1: To be utterly pedantic, the statement of the exercise does not define T(0V ). (The zero vector 0V of V is the sequence σ0 defined by σ0 (m) = 0 for all m, so it does not make sense to say “n is the largest integer such that σ0 (n) 6= 0.”) So if we want to be completely precise, we should f ...
... Remark 1: To be utterly pedantic, the statement of the exercise does not define T(0V ). (The zero vector 0V of V is the sequence σ0 defined by σ0 (m) = 0 for all m, so it does not make sense to say “n is the largest integer such that σ0 (n) 6= 0.”) So if we want to be completely precise, we should f ...
Notes
... If two angles are coterminal, the difference in their measures is 360° or a multiple of 360° Examples: Find the angle of smallest positive measure coterminal with an angle of the given measure. ...
... If two angles are coterminal, the difference in their measures is 360° or a multiple of 360° Examples: Find the angle of smallest positive measure coterminal with an angle of the given measure. ...
Linear Algebra and Matrices
... linear combination of the others. They define in space a smaller number of dimensions than the total number of vectors in the set. The resulting matrix will be rank-deficient and the determinant will be zero. Similarly, if all the elements of a line or column are zero, the determinant of the matrix ...
... linear combination of the others. They define in space a smaller number of dimensions than the total number of vectors in the set. The resulting matrix will be rank-deficient and the determinant will be zero. Similarly, if all the elements of a line or column are zero, the determinant of the matrix ...
