Assertion: matrix's root | /r/HasProperty | integer
Facets:
value: either again
type: MANNER
Source sentences:
text: While the square root of a nonnegative integer is either again an integer or an irrational number, in contrast an integer matrix can have a square root whose entries are rational, yet non-integral.
text: For example, the matrix ( 0 4 − 1 5 ) {\displaystyle \left({\begin{smallmatrix}0&4\\-1&5\end{smallmatrix}}\right)} has the non-integer square root ( 2 3 4 3 − 1 3 7 3 ) {\displaystyle \left({\begin{smallmatrix}{\frac {2}{3}}&{\frac {4}{3}}\\-{\frac {1}{3}}&{\frac {7}{3}}\end{smallmatrix}}\right)} as well as the integer square root matrix ( 2 − 4 1 − 3 ) {