[3.13] Find Matrix Minor And Adjoint - Texas Instruments TI-89 Tip List

expr(M[j,k])→list
[3.12] Don't use „list() „list() „list() „list() function in data editor
NOTE: this bug has been fixed in AMS 2.05. The „list() function can be used as a column function
definition.
In the Data/Matrix Editor, you can define functions in the header to create columns of entries. Refer to
the 89/92+ manual, page 248, for details. AMS 2.03 has a new function, „list(); see manual page
463.
Do not use this function in a column header. An Internal Error will result, and you will not be able to
modify or use the data variable, because Internal Errors will be the response to just about all actions on
the data variable. The only solution is to delete the data variable and start over again.
(credit to Eric Kobrin)

[3.13] Find matrix minor and adjoint

The 89/92+ have no built-in functions to find the minor and adjoint of a matrix, but these are easily
accomplished with the built-in functions. The minor of an n x n square matrix A = [a
of the matrix that results from deleting row i and column j of A. If the minor is
M ij
then the cofactor of a
( −1 ) i+j M ij = ✍ ij
and the adjoint of A is defined as
✍ 11 ✍ 21 ... ✍ n1
✍12 ✍ 22 ... ✍n2
adj ( A ) =
...
✍ 1n ✍ 2n ... ✍ nn
However, we need not find the minors and cofactors to find the adjoint, because of this identity:
adj(A) = A −1 $ A
It is faster to calculate the adjoint with this identity than by finding the minors and cofactors, but the
identity is true only if the matrix is non-singular. However, a singular matrix also has an adjoint. So, an
optimized adjoint function uses [1] if the matrix is singular, and [2] if not. This function finds the adjoint
of a matrix:
adjoint(m)
Func
©(m) Return adjoint of square matrix m
local k,n,i,j,d
is defined as
ij
... ... ...
A ! 0
if
] is the determinant
ij
[1]
[2]
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