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Há 11 horas · Explain: The original matrix equation is equivalent to a system of n×n linear equations in n×n variables. And there are n more linear equations from the fact that Q is a right stochastic matrix whose each row sums to 1. So it needs any n×n independent linear equations of the (n×n+n) equations to solve for the n×n variables.
Há 11 horas · If the inequality is not strict (that is, σ j ≥ j), then j is called a weak exceedance. The number of n-permutations with k exceedances coincides with the number of n-permutations with k descents. A record or left-to-right maximum of a permutation σ is an element i such that σ(j) < σ(i) for all j < i. Foata's transition lemma
Há 11 horas · A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
