Navigation Tree - Help

  "Math in ONE"

Reference Manual

      Contents

open   System Overview
open open Definitions
open open Algebra
open open (W) Statistics
open open (W)(AP) Matrices
open open Calculus
open open Unit Conveerter
open   Input data
open open Input Field, Memories & Expressions
open open Data Entry to Memory
open open (W)(AG) Import File
open open (W)(AP) Matrix Setup
open open (W)(AG) Export Data
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
open open SigFigs
open   Response to Customer Comments

"Math in ONE" Home

"Math in ONE" Download

Product Disclosure

Submit Comments Here


© Copyright "Math in ONE" 2011. All rights reserved

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.