In this parer, characterizations of inner product spaces are obtained by studyingpointwise properties of Pythagorean orthogonality in normed linear space, a quan-titative of the diference between Birkhof orthogonality and Pythagorean orthogo-nality,is given the existent of biorthogonality in Minkowski space is also discussed.A number of important conclusions results have been obtained by several re-searchers during their studying of properties of generalized orthogonalities of Minkows-ki space and the relationships between diferent kinds of generalized orthogonalities.but, their researches mainly focus on the following felds: the impact and the efecton the properties of Minkowski space by the properties of generalized orthogonalityin the entire space;on the other hand, the research of the relationship between thegeneralized orthogonalities is often qualitative. They mainly focus on two orthogo-nal if there is a diferent on this issue.And lack of quantitative characterizations ofthe real diferences.Based on all that have mentioned above, we frst proved that, We prove thata Minkowski plane X is an inner space if and only if there exists a non-zero P-orthogonally homogeneous element in X. As well as we show that in a Minkowskispace X, if some generalized orthogonality with existence and homogeneity impliesP-orthogonality, then X is an inner product space.Secondly, we depict intuitively the diference between Pythagorean orthogonaland Birkhof orthogonal in this article. From the perspective of quantitative, wedefne a constant P (X) with clear geometric properties. Through calculation, itproved that the scope of the P (X) and the contact with convexity in the spacewhen arrived upper bound. Also, we calculate the exact value of P (X) in theX=lp2space. |