Texas Instruments TI-89 User Manual - Page 795
Then A = X B X, and X = [V - eigenvalues
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cos( ) 2 X key cos(expression1) ⇒ expression cos(list1) ⇒ list cos(expression1) returns the cosine of the argument as an expression. cos(list1) returns a list of the cosines of all elements in list1. Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode setting. You can use ó , G o r ô to override the angle mode temporarily. In Degree angle mode: cos((p/4)ô ) ¸ cos(45) ¸ cos({0,60,90}) ¸ In Gradian angle mode: cos({0,50,100}) ¸ In Radian angle mode: cos(p/4) ¸ cos(45¡) ¸ ‡2 2 ‡2 2 {1 1/2 0} {1 ‡2 2 0} ‡2 2 ‡2 2 cos(squareMatrix1) ⇒ squareMatrix In Radian angle mode: Returns the matrix cosine of squareMatrix1. This is not the same as calculating the cosine of each element. When a scalar function f(A) operates on squareMatrix1 (A), the result is calculated by the algorithm: cos([1,5,3;4,2,1;6,ë2,1]) ¸ ..211620...... .205... .259... .121... .037... .248... ë.090... .218... 1. Compute the eigenvalues (li) and eigenvectors (Vi) of A. squareMatrix1 must be diagonalizable. Also, it cannot have symbolic variables that have not been assigned a value. 2. Form the matrices: l1 0 ... 0 B = 0 0 l2 ... 0 0 ...0 and X = [V1,V2, ... ,Vn] 0 0 ... ln 3. Then A = X B Xê and f(A) = X f(B) Xê. For example, cos(A) = X cos(B) Xê where: cos(λ1) 0 ... 0 cos (B) = 0 0 cos(λ2) ... 0... 0 0 0 0 ... cos(λn) All computations are performed using floatingpoint arithmetic. Appendix A: Functions and Instructions 795