13 Consecutive sums of two squares in arithmetic progressions 56:13 DORIAN GOLDFELD_ ORTHOGONALITY RELATIONS FOR COEFFICIENTS OF AUTOMORPHIC $L$-FUN 1:02:35 MORTEN RISAGER_ SHIFTED CONVOLUTION SUMS AND SMALL-SCALE MASS EQUIDISTRIBUTION A 1:06:43 A discrete mean value of the Riemann zeta function ...
What is r^n, spaces, and planes in linear algebra? What is the b in ax = b linear algebra? What is \mathbb{R}^2 in linear algebra? What does a_i mean in linear algebra? What is norm linear algebra geometrically? What is the zero vector in linear algebra? What is a nontrivial ...
Why does a basis for \mathbb{R}^n have to be linearly independent? Linear Algebra Find a basis for the solution space of the homogeneous linear system x - y + 2z = 0 2x + y = 0 x - 4y + 6z = 0 How can a basis not be orthogonal?
If vanishes then does not vanish, and the claim follows from the mean zero nature of ; similarly if vanishes. Hence we may assume that do not vanish, and then we can normalise them to equal . By completing the square it now suffices to show that whenever . As is on the quadratic ...
The orthogonal definition also has been extended to general use, meaning the characteristic of something being independent (relative to something else). It also can mean non-redundant, non-overlapping or irrelevant. Orthogonal lines and mathematics ...
The Jordan canonical form does not depend continuously on the matrix. For both quotes I did not remember the underlying reasons and since I do teach an introductory class on linear algebra this year, I got thinking about these issues again. Here is a very simple example for the fact in the...
In the case when the alphabet is the binary alphabet , and (for technical reasons related to the infamous non-injectivity of the decimal representation system) the string does not end with an infinite string of s, then one can reformulate the above universal construction by taking to be the ...
Curvature alone does not rule out an inner product. A space can have curvature but when you zoom into a tiny neighborhood of any point, then there are inner products, angles, right angles and orthogonal vectors. They are local to that point. As long as you have them, you should (judicio...
Conservation is assumed to be born in the phase, just as momentum is for instance. In other words, all known phenomena in physics are deterministic, classical and real, in the sense that information does propagate locally and experiments conducted statistically do hide latent variables....
What does it mean when the determinant is zero? It shows us that there is no solution to the linear equations that are represented by the matrix. This means that a Jacobian with a determinant of zero has no solutions. In other words, the robot gets stuck because the math “breaks” at...