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Inner product space is very rich in geometry.In this book we try to show some applications of inner product space in physics.Positive definite matrices are a very important class of matrices that appears frequently in the branch of mathematics as well as in physics. The set of n-by-n positive definite matrices are subclass of the set of matrices. Some of the important characterization and application of these types of matrices are being discussed here. For example, a positive definite matrix is a symmetric matrix whose eigenvalues are all positive, etc.