13th root 13th root Extracting the 13th root of a number is a famous category for the mental calculation world records. The challenge consists of being given a large number (possibly over 100 digits) and asked to return the number that, when taken to the 13th power, equals the given number. For example, the 13th root of 8,192 is 2 and the 13th root of 96,889,010,407 is 7. Extracting the 13th root has certain properties. One is that the 13th root of a number is much smaller: a 13th root will have approximately 1/13th the number of digits. Thus, the 13th root
Square root of a 2 by 2 matrix may have complex entries even if "M" is a real matrix; this will be the case, in particular, if the determinant "δ" is negative. When a matrix can be expressed as real multiple of the exponent of a matrix, formula_5 then the square root is formula_6 In this case the square root is real, and can be interpreted as the square root of a type of complex number. If "M" is an idempotent matrix, meaning that "MM" = "M", then if it is not the identity matrix its determinant is zero, and its trace equals its rank which (excluding the