  In this article, a comprehensive study is made on the continuity,
compactness, and spectrum of the lower triangular terraced matrix, introduced
by H. C. Rhaly, Jr. [Houston J. Math. 15(1): 137-146, 1989], acting on the
weighted null sequence spaces with bounded, strictly positive weights. Several
spectral subdivisions such as point spectrum, residual spectrum, and continuous
spectrum are also discussed. In addition, a new class of operator ideal
$\chi_{c_0(r)}^{(s)}$ associated to the Rhaly operator on weighted $c_0$ space
is defined using the concept of $s$-number and it is proved that under certain
condition, $\chi_{c_0(r)}^{(s)}$ forms a quasi-Banach closed operator ideal.
