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Definition of DETERMINANT
: an element that identifies or determines the nature of something or that fixes or conditions an outcome
: a square array of numbers bordered on the left and right by a vertical line and having a value equal to the algebraic sum of all possible products where the number of factors in each product is the same as the number of rows or columns, each factor in a given product is taken from a different row and column, and the sign of a product is positive or negative depending upon whether the number of permutations necessary to place the indices representing each factor's position in its row or column in the order of the natural numbers is odd or even
In linear algebra, a numerical value associated with a matrix having the same number of rows as columns. It is particularly useful in solving systems of (linear) equations and in the study of vectors. For a two-by-two matrix, the determinant is the product of the upper left and lower right terms minus the product of the lower left and upper right terms. Determinants of larger matrices involve more complicated arithmetic combinations of the terms and are usually solved using a calculator or computer.