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open open Input Field, Memories & Expressions
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open   Basic Operations
open open Function Expressions
open open (W)(AP) Matrix Expressions
open open Binary Expressions
open open Working with Memories
open open Variables use - Graphs
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Matrix Expressions

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 [1x1] matrix.

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:

  1. C[a,b] = A[a,b]+B[c,d] - matrix A and B size must be the same so a = c and b = d.
  2. 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.
  3. For function requirements refer to the program function descriptions popup display.

For matrix expressions, there are two unique operators defined in this program.

  1. ' < ' - use in a division operation to indicate right division A/B< = A*B-1 or if ' < ' is not present A/B = B-1*A. B-1 is a invers matrix of B.
  2. Explanation: Let 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.

  3. ' => ' - assignment operator, it must be the last operation in an expression or the last operation in a block.
    1. A+B=>C - =>C is last operation in expression; result of A+B will be stored in C.
    2. [A+B=>C]*A - =>C is last operation in block; result of A+B will be store in C.
    3. [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]*A will be store in D.
    4. [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 A+B.