Dihedral Group Frames with the Haar Property
... transform with respect to the canonical basis of Cn . The matrix T is diagonalizable and its Jordan canonical form is obtained by conjugating T by the discrete Fourier matrix. More 2(k−1)πi precisely if M = FT F−1 then the k th diagonal entry of M is given by Mkk = e n . Finally, it is worth noting ...
... transform with respect to the canonical basis of Cn . The matrix T is diagonalizable and its Jordan canonical form is obtained by conjugating T by the discrete Fourier matrix. More 2(k−1)πi precisely if M = FT F−1 then the k th diagonal entry of M is given by Mkk = e n . Finally, it is worth noting ...
Apprentice Linear Algebra, 3rd day, 07/06/05
... Example 3.5. Isometries of the plane (congruences) which fix the origin are linear maps. Examples include reflection across an axis that passes through the origin and rotation by a prescribed angle θ about the origin. Exercise 3.6. Prove that every congruence of the plane fixing the origin is either ...
... Example 3.5. Isometries of the plane (congruences) which fix the origin are linear maps. Examples include reflection across an axis that passes through the origin and rotation by a prescribed angle θ about the origin. Exercise 3.6. Prove that every congruence of the plane fixing the origin is either ...
VECTORS 1. Introduction A vector is a quantity that has both
... A vector is a quantity that has both magnitude and direction. This is in contrast to a (more familiar) scalar, which has only magnitude. Vectors are important as many quantities are direction-dependent; examples of vectors which you may have encountered include force, velocity and electric field. He ...
... A vector is a quantity that has both magnitude and direction. This is in contrast to a (more familiar) scalar, which has only magnitude. Vectors are important as many quantities are direction-dependent; examples of vectors which you may have encountered include force, velocity and electric field. He ...
Induction and Mackey Theory
... instead the C-span of it). Now, each CKgH ⊗ W is just CK · (gH ⊗ W ). Note that gH ⊗ W = g ⊗ W is a vector space since gh1 ⊗ w1 + gh2 ⊗ w2 = g ⊗ (h1 w1 + h2 w2 ). We can identify it with W by mapping gh ⊗ w 7→ hw. Moreover, both CK and gH ⊗ W are representations of Hg := K ∩ gHg −1 . We denote by Wg ...
... instead the C-span of it). Now, each CKgH ⊗ W is just CK · (gH ⊗ W ). Note that gH ⊗ W = g ⊗ W is a vector space since gh1 ⊗ w1 + gh2 ⊗ w2 = g ⊗ (h1 w1 + h2 w2 ). We can identify it with W by mapping gh ⊗ w 7→ hw. Moreover, both CK and gH ⊗ W are representations of Hg := K ∩ gHg −1 . We denote by Wg ...
Lecture 16 - Math TAMU
... to an n×n matrix A if B = S −1 AS for some nonsingular n×n matrix S. Remark. Two n×n matrices are similar if and only if they represent the same linear operator on Rn with respect to different bases. Theorem If A and B are similar matrices then they have the same (i) determinant, (ii) trace = the su ...
... to an n×n matrix A if B = S −1 AS for some nonsingular n×n matrix S. Remark. Two n×n matrices are similar if and only if they represent the same linear operator on Rn with respect to different bases. Theorem If A and B are similar matrices then they have the same (i) determinant, (ii) trace = the su ...