Yasar University Linear Algebra Calcultor Presentation

1. Yaşar University Linear Algebra Calculator Yusuf Yasin KumbulÖzlem Ece Çobanoğlu

2. 2 5 Conclusion 3 f 4 S OUTLINE 1 Introduction Matrix Operations Algorithms of the Program Software Usability

3. MATRIX ADDITION The sum A+B of two m-by-n matrices A and B is calculated like: (A + B)i,j = Ai,j + Bi,j, where 1 ≤ i ≤ m and 1 ≤ j ≤ n.

4. MATRIX SUBTRACTION The subtraction ofA-B of two m-by-n matrices A and B is calculated like: (A-B)i,j = Ai,j-Bi,j, where 1 ≤ i ≤ m and 1 ≤ j ≤ n.

5. MATRIX MULTIPLICATION Multiplication of A and B can calculated onlyif the number of columns of A equals the number of rows of B. Multiply therows of A by the columns of B.

6. SCALAR MULTIPLICATION The scalar multiplication cA of a matrix A and a number c is given by multiplying every entry of A by c: (cA)i,j = c · Ai,j.

7. TRACE OF A MATRIX The trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal of A. tr(T)= -2 + 1 -1 = -2

8. TRANSPOSE OF A MATRIX The transpose of an m-by-n matrix A is the n-by-m matrix AT (also denoted Atr or tA) formed by turning rows into columns and vice versa: (AT)i,j = Aj,i.

9. HISTORY OF JAVA JAVA was developed by James Gosling and his team at Sun Computers in the early 1990s. Acronym for the names of the team members: James Gosling, Arthur Van Hoff, and Andy Bechtolsheim Inspired by a coffee bean

10. JAVA FEATURES Platform Independent Simple Object Oriented Portable Dynamic Secure Multithreaded

11. Algorithms of Addition If(ARowSize==BRowSize && AColumnSize==BColumnSize){ for(int i =0; i<ARowSize; i++){ for(int j =0; j<AColumnSize; j++){ Array[i][j]=A[i][j]+B[i][j]; } } }

12. Algorithm of Subtraction If(ARowSize==BRowSize && AColumnSize==BColumnSize){ for(int i =0; i<ARowSize; i++){ for(int j =0; j<AColumnSize; j++){ Array[i][j]=A[i][j]-B[i][j]; } } }

13. Algorithm of Multiplication If(AColumnSize==BRowSize) for (int i=0; i < ARowSize; i++){ for (int j=0; j < BColumnSize; j++){ for (int p=0; p < AColumnSize; p++){ Array[i][j] += A[i][p]*B[p][j]; } } }

14. Algorithm of Scaler Multiplication for(int i =0; i<ARowSize; i++){ for(int j =0; j<AColumnSize; j++){ Array[i][j]=k*(A[i][j]); } } (k is a constant)

15. Algorithm of Trace if(AColumnSize==ARowSize){ for(int i =0; i<AColumnSize; i++){ sum+=A[i][i]; } }

16. Algorithm of Transpose for(int i =0; i<ARowSize; i++){ for(int j=0; j<AColumnSize; j++) Array[j][i]=A[i][j]; }

17. Software Usability Make a different approach for the program Every user can easily use Serious debugging and test process Eliminate all possible problems that user could face

18. Items on the Menu Bar About:Givesinformation about the program Languages: Provides selection between Turkish and English languages Separator Setting: Selects the desired separator for the numbers in the matrix Log: All process during the calculations done by the user Help: Gives all the details to use the program appropriately

19. Items on the Tool Bar Multiplication: Gives three choices to user, (Multiplication, Scaler Multiplication, Power) Addition: Adds any size of matrices Subtraction: Subtracts any size of matrices Trace: Gives the trace of any square matrix Transpose: Takes tranpose of any matrix Inverse: Takes inverse of any matrix Determinant: Takes determinant of any matrix

20. Logo of Yasar Universty Logo of Yasar University connects the user the main page of Yasar University website.

21. Enter the input of the matrices to Matrix A and Matrix B. Clear: Erases the number in the Text Area Random: 1) Assigns the number of the matrices at given row and column size, 2) Creates identity matrix at given size 3) Creates zero matrix at given row and column size

22. B to A: copies all data in the Matrix B to Matrix A A to B: copies all data in the Matrix A to Matrix B Output to A: copies all data in the Output Matrix to Matrix A Output to B: copies all data in the Output Matrix to Matrix B

23. Keep Output: Saves at most the 5 output in the memory Write to File: Writes all the outputs calculated by user to a text file Exit: Finishes the programme

24. DEBUGGING Some unexpected errors occurs because of usage. A good software guide the user to find the right way to enter valid input In the design of the programme, the label at the bottom of the frame gives the rules of specific operations.

25. DEBUGGING The programme gives an error massage when the user enters invalid matrix sizes for operations such as “The number of columns in A is not equal to number of rows in B!” If the user enter missing elements to a row or column. For instance, for a size of 3 x 3, the user enters 2 numbers for a row, it warns the user to see the mistake!

26. CONCLUSION Consider carefully and deeply about all the unexpected mistakes that can be occur while running the program and always find an alternative way to deal with the problems!

27. Thank You! http://www.yasar.edu.tr Özlem Ece Çobanoğlu Yusuf Yasin Kumbul