Assertion: matrix's root | /r/HasProperty | square
Facets:
Source sentences:
text: For example, the matrix ( 33 24 48 57 ) {\textstyle \left({\begin{smallmatrix}33&24\\48&57\end{smallmatrix}}\right)} has square roots ( 1 4 8 5 ) {\textstyle \left({\begin{smallmatrix}1&4\\8&5\end{smallmatrix}}\right)} and ( 5 2 4 7 ) {\textstyle \left({\begin{smallmatrix}5&2\\4&7\end{smallmatrix}}\right)} , as well as their additive inverses.
text: In general, a matrix can have several square roots.
text: A 2×2 matrix with two distinct nonzero eigenvalues has four square roots.
text: Some matrices have no square root.
text: Convergence is not guaranteed, even for matrices that do have square roots, but if the process converges, the matrix Y
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: Just as with the real numbers, a real matrix may fail to have a real square root, but have a square root with complex-valued entries.