In multivariate statistical analysis, it is a necessity to know the facts regarding the covariance matrix of the data in hand before applying any further analysis. This study focuses on testing hypotheses concerning the covariance matrices of multivariate normal data having the number of variables larger than or equal to the sample size, called high-dimensional data. The two objectives of this study were: first, for one sample data, to develop a test statistic for testing the hypothesis for whether the covariance matrix equals a specified known ...