This text discusses positive definite matrices and their completions. A matrix A is positive definite if it is symmetric and for all non-zero vectors x, x^T A x > 0. It is also equivalent that all principal minors of A are positive. A partial matrix B is a partial positive definite matrix if every fully specified principal submatrix is positive definite, and if an entry b_ij is specified, then so is b_ji and they are equal. A pattern Q has a positive definite completion if the principal subpattern determined by the diagonal positions of Q also has a positive definite completion. A pattern with all diagonal positions has a positive definite completion if its pattern-graph is chordal. Examples are given of patterns that do and do not have positive definite completions. The reference [GJSW] provides a study on positive definite completions of partial Hermitian matrices.This text discusses positive definite matrices and their completions. A matrix A is positive definite if it is symmetric and for all non-zero vectors x, x^T A x > 0. It is also equivalent that all principal minors of A are positive. A partial matrix B is a partial positive definite matrix if every fully specified principal submatrix is positive definite, and if an entry b_ij is specified, then so is b_ji and they are equal. A pattern Q has a positive definite completion if the principal subpattern determined by the diagonal positions of Q also has a positive definite completion. A pattern with all diagonal positions has a positive definite completion if its pattern-graph is chordal. Examples are given of patterns that do and do not have positive definite completions. The reference [GJSW] provides a study on positive definite completions of partial Hermitian matrices.