A Mathematical Proof to the HKLam Theory by Linear/Tensor Algebra and Analysis

In the previous papers, I have mentioned several times of HKLam Theory and their everyday usage but without the abstract mathematical proof. In order to remediate the flaws, I am now trying to proof the theory through both Tensor Algebra and Analysis as well as the statistical inference in this present paper. Indeed, people always say that mathematicians are linear animals or participate much in the subject of linear algebra while the British Scientist Newton observed a falling apple and discovered the gravity together with the development of calculus. In a similar case, my proof in the part of tensor algebra will be an analogy to the linear mapping, transformation etc while there are the corresponding corollary real physical life cases – 2 to 3 dimensional vectors calculus or even higher dimension of tensor analysis. Indeed, my proof will be based on the order two tensor but the HKLam theory may be extended up to nth order tensor but NOT applicable to the topic of the planned politics or even economics etc.The main aim is to show the proof of HKLam Theory by linear/Tensor algebra together with some applications in fluid dynamic and stress tensor field etc