Visualizing a determinant identity
The previous post discussed an algorithm developed by Charles Dodgson (better known as Lewis Carroll) for computing determinants. The key identity for proving that Dodgson’s algorithm is correct involves the Desnanot-Jacobi identity from 1841. The identity is intimidating in its symbolic form and yet easy to visualize. In algebraic form
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Read moreHow Lewis Carroll computed determinants
Charles Dodgson, better known by his pen name Lewis Carroll, discovered a method of calculating determinants now known variously as the method of contractants, Dodgson condensation, or simply condensation. The method was devised for ease of computation by hand, but it has features that make it a practical method for
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Read moreGram matrix
An elegant algebraic identity says If x is the vector [a b] and y is the vector [c d] then this identity can be written where the dot indicates the usual dot product. I posted this on Twitter the other day. Gram matrix Now suppose that x and y are
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