"Math in ONE"
Matrix expressions are evaluated in a separate mode independent from any scalar computation.
All rules that are applied to scalar expression are valid in matrix mode.
There are six matrices ([A] to [F]) that are available for the user to work with. These matrices can be configured in Matrix setup window or imported.
Square brackets ' [ ] ' are used in any matrix expression. Round brackets ' ( ) 'are reserved exclusively for scalar expressions.
Multiplication is the only operator defined to operate with scalar expression and matrix. In a matrix mode,
any scalar expression, function or number must be enclosed by round brackets
(e.g. (3)*A, A*(sin1.2), (3+ln2.1)*A+B).
If the result from a matrix expression evaluation is a number (e.g. determinant, multiplication of a row
and a column matrix), it is considered as
In a Matrix notation
A[RxC]: R represents the number of rows and C represents the number of columns.
R and C describe the size of the matrix. Some matrix functions require an input parameter that
specifies a row or column
(e.g col[A, nth column] , row[B, mth row]).
It is very important to recognize, that the incorrect matrix size in the expression will generate a FATAL ERROR. The following descriptions define correct matrix sizes for addition and multiplication operations:
C[a,b] = A[a,b]+B[c,d]- matrix A and B size must be the same so
a = cand
b = d.
C[a,d] = A[a,b]*B[c,d]- number of columns in A must be equal to number of rows in B so
b = c.
For matrix expressions, there are two unique operators defined in this program.
A/B< = A*B-1or if ' < ' is not present
A/B = B-1*A. B-1 is a invers matrix of B.
A/B = C therefore
A = B*C or A = C*B therefore
B-1*A = B-1*B*C or A*B-1 = C*B*B-1. By definition:
B*B-1 = B-1*B = I. I is unit matrix and
C*I = I*C = C.
A+B=>C- =>C is last operation in expression; result of
A+Bwill be stored in C.
[A+B=>C]*A- =>C is last operation in block; result of
A+Bwill be store in C.
[A+B=>C]*A=>D- =>C is the last operation in a block; result of A+B will be store in C. =>D is the last operation in an expression; result of
[A+B]*Awill be store in D.
[A+B=>C]*A=>D+C- will generate ERROR, =>D is neither the last operation in a block nor the last operation in an expression. The correct form will be:
[[A+B=>C]*A=>D]+C, now =>D is the last operation in a block. Notice
" ]+C "in the last expression: C in this location is equal to