Notes on Elementary Linear Algebra
... There also exist non-linear functions f : U → V which are additive but do not have the scaling property for all real scalars; however, these are more difficult to construct. One reason it can get messy is that Lemma 3.5 shows the scaling property must work for all rational scalars, so in such an exam ...
... There also exist non-linear functions f : U → V which are additive but do not have the scaling property for all real scalars; however, these are more difficult to construct. One reason it can get messy is that Lemma 3.5 shows the scaling property must work for all rational scalars, so in such an exam ...
Strict Monotonicity of Sum of Squares Error and Normalized Cut in
... but they both enjoy approximation algorithms which are quite successful in applications. A principal area of research for these functionals is model validation, i.e. choosing a correct number of clusters. It is easy to empirically observe, on a given set of points, that the minimum Sum of Squares Er ...
... but they both enjoy approximation algorithms which are quite successful in applications. A principal area of research for these functionals is model validation, i.e. choosing a correct number of clusters. It is easy to empirically observe, on a given set of points, that the minimum Sum of Squares Er ...
AND PETER MICHAEL DOUBILET B.Sc., McGill University 1969)
... A somewhat more detailed introduction to the contents of the thesis can be found at the beginning of each of the three parts. A kcknowledgement is now due to the two people whose help has been most useful to me in the completion of this work. The ideas, suggestions, and encouragement of Doctor Gian- ...
... A somewhat more detailed introduction to the contents of the thesis can be found at the beginning of each of the three parts. A kcknowledgement is now due to the two people whose help has been most useful to me in the completion of this work. The ideas, suggestions, and encouragement of Doctor Gian- ...
Lecturenotes2010
... The number of iterations kn to solve the n × n discrete Poisson problem using the methods of Jacobi, Gauss-Seidel, and SOR (see text) with a tolerance 10−8 . . . . . . . . . . . . . . . . . . . . . . . Spectral radia for GJ , G1 , Gω∗ and the smallest integer kn such that ρ(G)kn ≤ 10−8 . . . . . . . ...
... The number of iterations kn to solve the n × n discrete Poisson problem using the methods of Jacobi, Gauss-Seidel, and SOR (see text) with a tolerance 10−8 . . . . . . . . . . . . . . . . . . . . . . . Spectral radia for GJ , G1 , Gω∗ and the smallest integer kn such that ρ(G)kn ≤ 10−8 . . . . . . . ...
On the existence of equiangular tight frames
... (1) (Orthonormal Bases). When N = d, the sole examples of ETFs are unitary (and orthogonal) matrices. Evidently, the absolute inner product α between distinct vectors is zero. (2) (Simplices). When N = d + 1, every ETF can be viewed as the vertices of a regular simplex centered at the origin [7,17]. ...
... (1) (Orthonormal Bases). When N = d, the sole examples of ETFs are unitary (and orthogonal) matrices. Evidently, the absolute inner product α between distinct vectors is zero. (2) (Simplices). When N = d + 1, every ETF can be viewed as the vertices of a regular simplex centered at the origin [7,17]. ...
