# Is there any meaning for a density operator if we omit the j-th row and column in quantum mechanics?

Assume we have a density operator (Hermitian, PSD, with trace 1, where PSD means positive semi-definite) called A for a particle. $$v_i$$ shows the i-th eigenvector of A and $$\lambda_i$$ shows the i-th eigenvalue. I assume that the elements of $$|v_{i}|^2$$ form a probability distribution of the particle being in the state $$i$$, and $$\lambda_i$$ shows the probability of happening the i-th state. Now if we omit the j-th row and column of A (called $$A_{-j}$$, is there any intuition behind the obtained matrix and its eigenvalues?