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Tag Archives: angle
In philosophical debates about absolute truth, people cite “the truths of pure mathematics” as beyond reproach—eternal and universal things discovered/invented by us fallible mortals. But the more deeply I look into these issues myself, the more I see evidence that … Continue reading
Angle = Volume
This is trippy, and profound. The determinant — which tells you the change in size after a matrix transformation 𝓜 — is just an Instance of the Alternating Multilinear Map. (Alternating meaning it goes + − + − + − + … Continue reading
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Tagged abstract, angle, deep, determinant, differential form, direction, linear algebra, linear operator, linear transforms, mapping, math, mathematics, maths, matrix, multilinear map, shape, size, tensor, trippy, vector, volume
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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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Circles
A circle is made up of points equidistant from the center. But what does “equidistant” mean? Measuring distance implies a value judgment — for example, that moving to the left is just the same as moving to the right, moving forward … Continue reading
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Tagged angle, circle, education, geometry, Henri Poincaré, imagination, long reads, Lp norm, L_p norm, math, mathematics, maths, metric, metric spaces, metrics, noncommutative, norm, norms, Poincaré disk, size
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Vectors
Vectors, concretely, are arrows, with a head and a tail. If two arrows share a tail, then you can measure the angle between them. The length of the arrow represents the magnitude of the vector. The modern abstract view is … Continue reading
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Tagged angle, corpus, cryptography, education, field, force, Fourier series, functional analysis, generalised number, generalised numbers, jpeg, linear algebra, linear transforms, long reads, math, mathematics, maths, number, Photoshop, science, shearing, signal analysis, Taylor series, thermodynamics, vectors
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