Joe Root his first golden duck in his ODI career. The 5th ODI was better for Root as he scored a quick 21 before being bowled and also took the wicket of George Bailey. England lost the series 2–1 and Root finished the series with 36 runs and 1 wicket. Root was selected for the 2013-14 Ashes series. He was selected at number 6 for the first Test as Michael Carberry was given the opening batsman role alongside Alastair Cook. Root only managed 2 runs from 7 balls in the first innings before being caught off a Mitchell Johnson delivery. In the
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