Hp 49g+ User Manual download pdf (Page 335)

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For square matrices of higher order determinants can be calculated by using

smaller order determinant called cofactors. The general idea is to “expand” a

determinant of a n×n matrix (also referred to as a n×n determinant) into a sum

of the cofactors, which are (n-1)×(n-1) determinants, multiplied by the elements

of a single row or column, with alternating positive and negative signs. This

“expansion” is then carried to the next (lower) level, with cofactors of order (n-

2)×(n-2), and so on, until we are left only with a long sum of 2×2

determinants. The 2×2 determinants are then calculated through the method

shown above.

The method of calculating a determinant by cofactor expansion is very

inefficient in the sense that it involves a number of operations that grows very

fast as the size of the determinant increases. A more efficient method, and

the one preferred in numerical applications, is to use a result from Gaussian

elimination. The method of Gaussian elimination is used to solve systems of

linear equations. Details of this method are presented in a later part of this

chapter.

To refer to the determinant of a matrix A, we write det(A). A singular matrix

has a determinant equal to zero.

Function TRACE

Function TRACE calculates the trace of square matrix, defined as the sum of

the elements in its main diagonal, or

∑

atr

)(A .

Examples:

1 2 ... 330 331 332 333 334 335 336 337 338 339 340 ... 861 862

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Hp 49g+ User Manual Page 335

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