Astrolog
Big O notation is useful when analyzing algorithms for efficiency For example, the time (or the number of steps) it takes to complete a problem of size n might be found to be T(n) = 4n 2 − 2n 2As n grows large, the n 2 term will come to dominate, so that all other terms can be neglected—for instance when n = 500, the term 4n 2 is 1000 times as large as the 2n termMatrix A If Ais m n, then Ax = 2 6 6 6 4 Row 1(A) Row 2(A) Row m(A) 3 7 7 7 5 x = 2 6 6 4 Row 1(A)x Row 2(A)x Row m(A)x 3 7 7 7 5 Each of these products is the \dot product" of a row of Awith the vector x To show the desired result, let x 2Null(A) Then each of the products shown in the equation above must be zero, since Ax = 0, so
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