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Tag Archives: matrices
How to multiply matrices
This is for my homies in math class. Mathematical matrices are blocks of numbers, arrayed in 2D. (Higherdimensional arrays are called tensors.) Left “times” right equals target. Each entry in the target is the result of a series of +’s … Continue reading
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Tagged 2D, angle, array, econometrics, inner product, linear algebra, linear operators, math, mathematics, maths, matrices, matrix multiplication, numbers, ODE's, operators, systems of differential equations, tensor, vectors
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Determinant
A matrix ℳ represents a sequence of + and × operations. At the end you’ve linearly transformed a space (sheared it, expanded it, rotated it — but kept the origin where it is.) Did the amount of stuff in the picture change when you … Continue reading
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Tagged determinant, econometrics, linear algebra, math, mathematics, maths, matrices
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What is an eigenvector?
The eigenvectors of a matrix summarise what it does. Think about a large, notsparse matrix. A lot of computations are implied in that block of numbers. Some of those computations might overlap each other—2 steps forward, 1 step back, 3 steps … Continue reading
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Tagged affine, econometrics, education, eigenvalue, eigenvector, eigenvectors, function, helicopters, images, linear algebra, math, mathematics, maths, matrices, Photoshop, rotation, science, shear, transformations, transforms
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In the loop quantum gravity approach, spacetime is quantized by a procedure that encodes it in a discretized structure, consisting of spin networks and spin foams. A spin network consists of an oriented embedded graph in a 3dimensional manifold with … Continue reading
Image
February 18, 2011
Tagged art, general relativity, graph theory, group theory, groups, heroes, homotopy, loop quantum gravity, manifolds, math, mathematics, maths, matrices, matrix algebra, parallel transport, quantization, science, spacetime, special unitary group, spin foam, spin network, SU(2), tetrad, tetrads, vierbein, wizardry
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Vierergruppe
Any four things in order ABCD can be rearranged. You could do ACBD — middle swap — 1324 DBCA — end swap — 4231 BCDA — rotation — 2341 for example. Let’s say the four things are the four corners … Continue reading
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Tagged abelian groups, Bryan Hayes, education, Felix Klein, group theory, isomorphism, math, mathematics, maths, matrices, Niels von Abel
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