Inquiry about ideal library was sought by interdisciplinary approach from human competence derived from performance engineering by Gilbert (1978), and the library information policy by Wilson (1977). With Wilson's insights into the field of library and information science (LIS), this work demonstrated the synthesis of Wilson and Gilbert: engineering as common ground. One of the central concerns in LIS, utilization of knowledge, is re-conceptualized as Gilbert's view of performance, which reflected at different vantage points. Four leisurely theorems are introduced for his view of performance engineering, which produce human competence. The performance matrix is the application tool that represents Gilbert's theorems of performance engineering. It is used to clarify vantage points about the library, and constructed a model of the performance engineering system of ideal library. Based upon the model, two applications were made. One is to apply the performance matrix to the existing academic library. Another is to apply the performance matrix for building a special collection. These two applications show that the performance matrix is capable to analyze existing performance system as well as designing and building a performance system.