Lecture2
... Elementary row and column operations • The following operations applied to the augmented matrix [A|b], yield an equivalent linear system – Interchanges: The order of two rows/columns can be changed ...
... Elementary row and column operations • The following operations applied to the augmented matrix [A|b], yield an equivalent linear system – Interchanges: The order of two rows/columns can be changed ...
Slides
... Sketching to solve l1-regression How to find an approximate solution x to minx |Ax-b|1 ? Want x‘ for which if x‘ is solution to minx |(SA)x-(Sb)|1 , then |Ax‘-b|1 · (1+ε) minx |Ax-b|1 with high probability For d log d x n matrix S of Cauchy random variables: |Ax‘-b|1 · (d log d) minx |Ax-b|1 ...
... Sketching to solve l1-regression How to find an approximate solution x to minx |Ax-b|1 ? Want x‘ for which if x‘ is solution to minx |(SA)x-(Sb)|1 , then |Ax‘-b|1 · (1+ε) minx |Ax-b|1 with high probability For d log d x n matrix S of Cauchy random variables: |Ax‘-b|1 · (d log d) minx |Ax-b|1 ...
1 Smooth manifolds and Lie groups
... Let k = R, C. For an n × n matrix A, kAk = sup |Ax|. |x|=1 ...
... Let k = R, C. For an n × n matrix A, kAk = sup |Ax|. |x|=1 ...
Math 215 HW #9 Solutions
... both sides of the above equation, we see that det A = λ1 λ2 · · · λn , so the determinant of A is equal to the product of the eigenvalues of A. ...
... both sides of the above equation, we see that det A = λ1 λ2 · · · λn , so the determinant of A is equal to the product of the eigenvalues of A. ...
