determinánsának

The term "determinánsának" is the genitive singular form of the Hungarian word "determináns," which translates to "determinant" in English. In mathematics, a determinant is a scalar value that can be computed from the elements of a square matrix. It is a fundamental concept in linear algebra with numerous applications. The determinant of a matrix provides important information about the matrix itself. For example, a matrix is invertible if and only if its determinant is non-zero. The determinant also geometrically represents the scaling factor of the linear transformation described by the matrix. For a 2x2 matrix [[a, b], [c, d]], the determinant is calculated as ad - bc. For larger square matrices, the determinant can be computed using cofactor expansion or other methods. The genitive case "determinánsának" would typically be used in a sentence to indicate possession or a relationship, such as "a mátrix determinánsának kiszámítása" which translates to "the calculation of the matrix's determinant." This grammatical form emphasizes that the determinant belongs to or is associated with a specific matrix.