I move my arm. [holonomy] I move my arm, hand and shoulder. [holonomy] I move my arm, hand, shoulders, but my fingers are still. I move my arm. [lie group] I move my arm across the table. [embedded in a … Continue reading
@IgorCarron blogs recent applications of compressive sensing and matrix factorisation every week. (Compressive sensing solves underdetermined systems of equations, for example trying to fill in missing data, by L₁-norm minimisation.) This week: reverse-engineering biochemical pathways and complex systems analysis. (Source: … Continue reading
May 28, 2012
Tagged adjacency matrix, applied mathematics, biochemistry, biology, chemistry, complex networks, compressed sensing, compressive sensing, dynamical systems, graph theory, Igor Carron, L₁ norm, matrices, matrix algebra, matrix factorisation, matrix factorization, networks, synthetic biology, time series, topography
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Once you’re comfortable with 2-arrays and 2-matrices, you can move up a dimension or two, to 4-arrays or 4-tensors. You can move up to a 3-array / 3-tensor just by imagining a matrix which “extends back into the blackboard”. Like … Continue reading
Tagged 4-D, array, data, linear transformations, matrices, matrix, matrix algebra, object orientation, object-oriented programming, R, tensor
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Linear Transformations will take you on a Trip Comparable to that of Magical Mushroom Sauce, And Perhaps cause More Lasting Damage Long after I was supposed to “get it”, I finally came to understand matrices by looking at the above … Continue reading
Tagged algebra, eigenvector, eigenvectors, linear algebra, linear transformations, math, mathematics, maths, matrices, matrix algebra, matrix transformations, vector, vector calculus, vectors
Mathematical matrices are blocks of numbers. So they don’t necessarily have definite characteristics the way plain vanilla, singleton numbers do. They’re freer. For example 131 ∈ positive and −9 ∈ negative. But is positive, negative, or zero? Well, it has … Continue reading