Notes - Cornell Computer Science
... but Q will preserve norm, dot products, etc. at the same time! This makes this factorization very suitable for questions where norm is important, and leads to better (more accurate) methods for least squares problems. Preview: one other difference is that QR can be applied to non-square matrices, re ...
... but Q will preserve norm, dot products, etc. at the same time! This makes this factorization very suitable for questions where norm is important, and leads to better (more accurate) methods for least squares problems. Preview: one other difference is that QR can be applied to non-square matrices, re ...
Solutions, PDF, 37 K - Brown math department
... The matrix is right invertible. If it is left invertible, it is invertible and its right inverse is unique (and coincide with the inverse). But we have more than one right inverse, so the matrix cannot be left invertible. 2. Find all left inverses of the column (1, 2, 3)T Solution: (x, y, 1/3 − x/3 ...
... The matrix is right invertible. If it is left invertible, it is invertible and its right inverse is unique (and coincide with the inverse). But we have more than one right inverse, so the matrix cannot be left invertible. 2. Find all left inverses of the column (1, 2, 3)T Solution: (x, y, 1/3 − x/3 ...
Notes on fast matrix multiplcation and inversion
... we have assumed that the running time is non-decreasing in n and used M (2n) ≤ 23 M (n) from the assumption that M (n) ≤ n3 . We also make several other assumptions that are less obvious. A square matrix B is symmetric if it is equal to its transpose, B T = B. A symmetric matrix B is positive defin ...
... we have assumed that the running time is non-decreasing in n and used M (2n) ≤ 23 M (n) from the assumption that M (n) ≤ n3 . We also make several other assumptions that are less obvious. A square matrix B is symmetric if it is equal to its transpose, B T = B. A symmetric matrix B is positive defin ...
Matrix manipulations
... From your linear algebra background, you should know a matrix as a representation of a linear map. A matrix can also represent a bilinear function mapping two vectors into the real numbers (or complex numbers for complex vector spaces): (v, w) → w∗ Av. Symmetric matrices also represent quadratic for ...
... From your linear algebra background, you should know a matrix as a representation of a linear map. A matrix can also represent a bilinear function mapping two vectors into the real numbers (or complex numbers for complex vector spaces): (v, w) → w∗ Av. Symmetric matrices also represent quadratic for ...
4-2 Quadratic Equations
... BASEBALL Suppose a baseball was 3 feet above the ground when it was hit straight up with an initial velocity of 60 feet per second. The function d(t) = 60t - 16t2 + 3 gives the ball’s height above the ground in feet as a function of time in seconds. How long did the catcher have to get into position ...
... BASEBALL Suppose a baseball was 3 feet above the ground when it was hit straight up with an initial velocity of 60 feet per second. The function d(t) = 60t - 16t2 + 3 gives the ball’s height above the ground in feet as a function of time in seconds. How long did the catcher have to get into position ...
Condition estimation and scaling
... Furthermore, multiplying by an explicit inverse is almost exactly the same amount of arithmetic work as a pair of triangular solves. So computing and using an explicit inverse is, on balance, more expensive than simply solving linear systems using the LU factorization. To make matters worse, multipl ...
... Furthermore, multiplying by an explicit inverse is almost exactly the same amount of arithmetic work as a pair of triangular solves. So computing and using an explicit inverse is, on balance, more expensive than simply solving linear systems using the LU factorization. To make matters worse, multipl ...
