Hp 50g Graphing Calculator Manual do Utilizador descarregar pdf (Página 341)

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Page 11-14

Function TRACE

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

elements in its main diagonal, or

Examples:

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.

∑

atr

)(A

1 2 ... 336 337 338 339 340 341 342 343 344 345 346 ... 886 887

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