If the diagonal elements of the "Th-matrix" are replaced by non-zero real numbers, then it becomes a normal diagonal matrix and a normal diagonal matrix is a Multiplicative Group. Then the "Th-matrix" has some practical applications. For example, if we replaced the diagonal elements with 17 daily closing prices of 17 funds, such as: DIA, FBALX,… SPY, then we formed a Th-Market Diagonal Matrix that expresses the 17-fund market.

DIAis the Do Jones Industrial Average, SPY is the Standard & Poor 500 ETF

For arangeland, the components would be plant species, Chinese grassland, would be STIPA, LEYMUS, SALSOLA,…

For Fort Carson Land Condition Trend Analysis, they would be: Bromus, Bouteloua, Yucca, Pinus, etc.

For anti-random test EE, they would be for example, 6-bit numbers.

Here we are using stock market variables, as these are the huge data set updated timely, accurate, accessible by anyone, and most important charge free,.