Normal Completions Of A Block Partial Matrix

The main purpose of this thesis is to study normal completion of partial matrices. Given a partial matrix, if we can retain the prescribed entries and specify the free entries so that the resulting matrix is normal, then we say that the partial matrix has a normal completion. One of the questionsasked by Bhatia and Choi is: Given a partial matrix N =(?), when does N has a normalcompletion? I discuss some situations and give some examples. Also I investigate the form of a general solution of N 's normal completion under the condition C = B~*.