matrix calculator

The matrix calculator supports a maximum of: 999×999 matrices (too large matrices are too time-consuming to initialize and calculate. To prevent unresponsiveness caused by misoperation, this version does not support it.
Four arithmetic operations use custom functions to ensure accuracy
There is no limit to the accuracy of addition, subtraction, and multiplication operations.
Operation precision including division: 250 decimal places, output precision: 200 decimal places (continuous operations will amplify the error, please try to avoid it)
Note: In division, numbers whose absolute value is less than 10 raised to the power of -200 will be treated as 0 (involving rank calculation and general solution operations)

As shown in the figure, the interface is divided into three parts: matrix input interface, control area, and output prompts. There are two matrices on the interface, and the program automatically disables or enables row and column parameters depending on what you choose to do. For example, if you select "Matrix Addition", the row and column parameters of Matrix 1 will be available, and the number of rows and columns of Matrix 2 will be automatically adjusted according to the changes in Matrix 1; if you select "Matrix Multiplication", the row parameters of Matrix 2 will not be changeable and will automatically match the matrix The column parameters for 1 remain the same. As shown below:

This is the effect after choosing to run "Matrix Multiplication". As you can see in the figure, the rows of matrix 2 cannot be changed and will automatically be synchronized with the columns of matrix 1, and the columns of matrix 2 can still be changed. The result after running will be a new matrix with the same number of rows as matrix 1 and the same number of columns as matrix 2. According to the default settings of the program, the output result after the operation will be sent to matrix 1, overwriting the original data, and clearing matrix 2 for the next operation.

2. Usage steps

The following demonstrates the use of Matrix by adding matrices and finding solutions to linear equations.
1.Matrix addition
First, we select "Matrix Addition" from the list in the lower right corner. At this time, the row and column parameters of matrix 2 will be automatically disabled and adjusted to a size suitable for matrix 1. As shown in the picture

Next, fill in the data in the two matrices respectively

Click the "Calculate" button

The result of the operation appears in matrix 1, and matrix 2 is cleared.

There will be corresponding prompts in the "Output Prompts" during all running steps, please pay attention to their instructions.

2. Solve linear equations
This time we are solving a system of non-homogeneous linear equations
2(x1)- (x2)+3(x3)+2(x4)=0
5(x1)- (x2)+11(x3)+2(x4)=-4
3(x1)- (x2)-5(x3)-3(x4)=6
(x1)-(x2)+11(x3)+7(x4)=-6
Enter the augmented matrix into matrix 1 as shown on the right
(Note: To solve a system of homogeneous linear equations, you also need to enter an augmented matrix, and the last column is all 0)


After clicking "Calculate", a set of solutions to the system of equations appears in Matrix 2. The first column is a special solution, and the subsequent columns form a basic solution system.
(This program does not round the results after the operation. If necessary, please do it yourself. If you need more requirements on operations and results, please use the Matrix Calculator Professional Edition)
As shown in the solution on the right, after rounding, it is
Special solution c1
0.5 1.25
-1.0625 3.09375
-0.6875 -0.46875
0 1

3. Precautions (Important)
Every time you change the rows and columns of the matrix, the matrix will be initialized and the original data will be cleared. Please set the matrix size first and then enter the data.
This matrix calculator performs decimal division with a precision of 250 digits and an output precision of 200 digits. Due to the continuous division and multiplication in the operations of finding the rank, solving the system of equations and finding the inverse matrix, the error may be expanded, and this calculator cannot guarantee its complete accuracy. (The 1.0L version has an operation accuracy of 1100 digits and an output accuracy of 1000 digits. At the same time, the operation time will be extended accordingly)
This matrix calculator limits the matrix size and only supports matrices up to 999×999. This limitation is due to the fact that it was found during testing that if the matrix size is changed, the initialization and operation of the matrix will be more time-consuming. To prevent long waits caused by incorrect input. (The 1.0L version does not have this restriction. If you have large matrix operation requirements and are not sensitive to operation time, please use the 1.0L version)
Features that the Matrix Calculator Professional Edition will support: multi-threading to increase calculation speed and prevent suspended animation in large-scale calculations; custom calculation precision and output precision, and support writing to files.