linear_app

Linear Algebra App (In Progress)

Demo Video: ...

TODO: Desgin and Implement Function

Done: CheckSpan, Check Linearly Independent, All in Comsubspace.m, Rows operations (Dswaprow, Dmulrow, Daddrow), RREF, Solve Unique Solutions.

Not Done: Ploting stuff; Determinant stuff (CramRule, FindDet); MLX Files: Span + Linear Trans + Subspace and Plot, EigenValue and EigenVector.

Classification: Matrix outputs text (good), Matrix outputs Matrix (good), Matrix outputs plots (hard one, do later)

Check for input exceptions later ...

Download and Open the App

Usable and but NOT Editable version

1. Download the linear_app_package_v7.mlappinstall by clicking download raw file button on the top right and double click to run.

Usable and Editable version

1. Download the Latest MATLAB Version:

   • Download the latest .mlapp file from the ./mlapp_design folder.

2. Open the App:

   • Double-click the downloaded .mlapp file to open it in MATLAB.
   • The app will open in the MATLAB App Designer environment.

General Steps

1. Input Matrix Dimensions:
   • Enter the number of rows in the "Rows" field.
   • Enter the number of columns in the "Cols" field.
   • Click the GenerateMatrix button to create a zero matrix of the specified dimensions. This will populate the matrix display area with editable cells.

Example: Initialize a 3x3 Matrix with all 0s

2. Enter Matrix Elements:
   • Manually enter the elements of the matrix in the editable cells under "Column 1", "Column 2", etc.
   • Invalid input will be appeared as NaN, and therefore the button cannot be used.
   • If applicable, enter the elements of the vector in the Vector b column.

Example: Manually enter elements in the matrix

Performing Operations

Row Operations

• Swap Rows:
  • Enter the indices of the rows to swap in the "RowSwap1" and "RowSwap2" fields.
  • Click the SwapRow button.
  • The results will be appeared in the original matrix above.

Example: Swap row 1 with row 2

• Multiply Row:
  • Enter the index of the row to multiply in the "RowToMultiply" field.
  • Enter the multiplication factor in the "MultiplyFactor" field.
  • Click the MultiplyRow button.
  • The results will be appeared in the original matrix above

Example: Multiple Row 2 with a factor of 2

• Add Multiple of Source Row to Destination Row:
  • Enter the index of the source row in the "SourceRow" field.
  • Enter the index of the destination row in the "DestinationRow" field.
  • Enter the multiplication factor in the "MultiplyFactor" field.
  • Click the AddMultipleOfSourceRowToDestinationRow button.
  • The results will be appeared in the original matrix above

Example: Add 2*Row1 to Row2

Matrix and Vector Operations

• Reduced Row Echelon Form (RREF):

  • Click the RREF button to transform the matrix to its reduced row echelon form.

• Solve Augmented Matrix:

  • Enter the elements of the vector in the Vector b column.
  • Click the SolveAugementedMatrix button to solve the system of linear equations represented by the augmented matrix.
  • This can only solve for unique solution, updates are needed for free varibables and infinite solutions.

• Check Span:

  • Enter the elements of the vector in the Vector b column.
  • Click the CheckSpan button to check if Vector b is in the span of the vector space.

• Check Linearly Independent:

  • Click the CheckLinearlyIndependent button to check if the vectors are linearly independent.

• Find Row Space Basis:

  • Click the FindRowSpaceBasis button to find the basis of the row space of the matrix.

• Find Column Space Basis:

  • Click the FindColSpaceBasis button to find the basis of the column space of the matrix.

• Find Null Space Basis:

  • Click the FindNullSpaceBasis button to find the basis of the null space of the matrix.

• Find Rank:

  • Click the FindRank button to find the rank of the matrix.

• Find Nullity:

  • Click the FindNullity button to find the nullity of the matrix.

Plotting Vectors

• Plot Column Vectors:

  • PlotColVectors can only plot two 3D vectors after clicking on FindColSpaceBasis.
  • Click the PlotColVectors button to plot the column vectors of the matrix.
  • The plotting result will be appeared in the plotting region as a plane in R3.

• Plot Single Vector:

  • Enter a 3D vector in Vector b Column.
  • Click the PlotSingleVector button to plot the vector Vector b.
  • If the Vector b is in the span, it will appeared as a orange vector on the span plane. Otherwise, it will be appeared as a blue vector.

Plotting Example:

1. Click on FindColSpaceBasis to get the basis as a two 3D vectors

2. Click on PlotColVectors to plot the span as a plane in R3

3. Enter a vector in Vector b and click PlotSingleVector to plot the Vector b in R3, in this example, the Vector b is not in the span so it appeared as a blue vector, as also checked by clicking on the CheckSpan button.

4. Enter a vector in Vector b and click PlotSingleVector to plot the Vector b in R3, in this example, the Vector b is in the span so it appeared as a orange vector, as also checked by clicking on the CheckSpan button.

Results

• The results of the operations will appear in the "Results" section at the bottom of the app.
  • If the result is a statement, it will appear in the "Results" box.
  • If the result is a matrix, it will appear in the matrix box under the "Results" section.
• The graphical representation (if applicable) will be shown in the plot area labeled "Title".

Additional Notes

• Ensure that the matrix and vector dimensions are correctly specified before performing any operations.
• Some operations may require additional inputs or conditions; refer to the specific button descriptions for details.

By following these instructions, you can utilize the MATLAB app to perform various linear algebra operations and visualize the results.