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A n×n matrix A is an orthogonal matrix if AA^(T)=I, (1) where A^(T) is the transpose of A and I is the identity matrix. In particular, an orthogonal matrix is always ...

The Pauli matrices, also called the Pauli spin matrices, are complex matrices that arise in Pauli's treatment of spin in quantum mechanics. They are defined by sigma_1 = ...

product_(k=1)^(infty)(1-x^k) = sum_(k=-infty)^(infty)(-1)^kx^(k(3k+1)/2) (1) = 1+sum_(k=1)^(infty)(-1)^k[x^(k(3k-1)/2)+x^(k(3k+1)/2)] (2) = (x)_infty (3) = ...

A prolate spheroid is a spheroid that is "pointy" instead of "squashed," i.e., one for which the polar radius c is greater than the equatorial radius a, so c>a (called ...

A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...

Rather surprisingly, trigonometric functions of npi/17 for n an integer can be expressed in terms of sums, products, and finite root extractions because 17 is a Fermat prime. ...

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

The regular polygon of 17 sides is called the heptadecagon, or sometimes the heptakaidecagon. Gauss proved in 1796 (when he was 19 years old) that the heptadecagon is ...