İlk başta iki matrix'in uzunluğunu alıyoruz sonra değerlerini alıyoruz her bir matrix'in.Sonrasında yapılacak işlem seçilir ve o işlem'e göre bir sonuç verilir.

d:Diagonal and Trace => square matrix olmak zorunda. diagonal =>bir köşegen çiz ve her köşegendeki elemanlar diagonalin elemanıdır. Trace ise diagonal elemanlarının toplamıdır.

i:Idempotent =>A^2==A yani karesi kendisine eşitse idempotent matrix tir. Idempotent matrix , square matrix olmak zorunda.

n:Nilpotent =>A^n==A yani üssü ne olursa olsun kendisine eşitse nilpotent matrix tir.Nilpotent matrix, square matrix olmak zorunda.

v:Involutive => A * A == I yani bir matrix in karesi birim matrise eşitse Involutive matrix tir.Involutive Matrix square olmak zorunda.

s:Symmetric => B^T == B ise symmetric ve symmetric square olmak zorunda eğer B^T == -B İSE ASSYMMETRİC VE SQUARE OLMAK ZORUNDA .

o:Orthogonal => A^T * A == I ise orthogonal matrix tir ve square olmak zorundadır .

p:Periodic => A^p+1==A ise periyodik matrix tir. Periyodu kullanıcı girmeli. square olmasına gerek yok.

UZUNLUGUNU ALIR MATRIXLERIN

System.out.println("Please enter the length of 2 matrixes: "); int n = input.nextInt(); int Matrix1 [][] = new int[n][n]; int Matrix2 [][] = new int[n][n];

İKİ MATRİX'İN DEĞERLERİNİ ALIR

for(int i=0;i<n;i++){ for(int j=0;j<n;j++){ System.out.printf("Enter a number to (%d,%d). first matrix element : ",i,j); Matrix1[i][j]=input.nextInt(); } } System.out.println("FIRST MATRIX:"); for(int i=0;i<n;i++){ for(int j=0;j<n;j++){ System.out.printf("%3d",Matrix1[i][j]); } System.out.println(); }

    for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
            System.out.printf("Enter a number to (%d,%d). second matrix element : ",i,j);
            Matrix2[i][j]=input.nextInt();
        }
    }
    System.out.println("SECOND MATRIX : ");
    for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
            System.out.printf("%3d",Matrix2[i][j]);
        }
        System.out.println();
    }

YAPILACAK İSLEMİ ALIR VE SEÇİLEN KARAKTERİ OPERATİON A ATAR.

Operations c = new Operations(); System.out.println("What do you want to do with this matrix or matrixes? :"); System.out.println("Sum => + / Subtraction => - / Multiplication => * / Diagonal and Trace => d / Symmetric or Asymmetric => s / Orthogonal matrix or not => o / Periodic matrix or not => p / Idempotent matrix or not => i / Nilpotent matrix or not => n / Involutive matrix or not => v ");

char operation = input.next().charAt(0);

OPERATION'A GORE İSLEM YAPAR.

switch(operation) { case '+': c.sum(Matrix1, Matrix2); break;

        case '-':  System.out.println(c.sub(Matrix1, Matrix2 )); break;
        
        case '*':  System.out.println(c.mult(Matrix1, Matrix2)); break;
        
        case 'd':  System.out.println("Please enter which matrix you want to use?(1/2): "); 
                   int choice1 = input.nextInt();
                   if(choice1 == 1) {
                    c.diagonalANDtrace(Matrix1);
                   }
                   else if(choice1 == 2) {
                    c.diagonalANDtrace(Matrix2);
                   } break;
                   
        case 'i': System.out.println("Please enter which matrix you want to use?(1/2): ");
                  int choice2 = input.nextInt();
                  if(choice2 == 1) {
                    System.out.println(c.isIdempotent(Matrix1));
                  }
                  else if(choice2 == 2) {
                    System.out.println(c.isIdempotent(Matrix2));
                  } break;
                  
        case 'n': System.out.println("Please enter which matrix you want to use?(1/2): ");
                  int choice3 = input.nextInt();
                  if(choice3 == 1) {
                  System.out.println(c.isNilpotent(Matrix2));
                  }
                  else if(choice3 == 2) {
                  System.out.println(c.isNilpotent(Matrix2));
                  } break;
                  
        case 'v': System.out.println("Please enter which matrix you want to use?(1/2): ");
                  int choice4 = input.nextInt();
                  if(choice4 == 1) {
                  c.isInvolitive(Matrix1);;
                  }
                  else if(choice4 == 2) {
                  c.isInvolitive(Matrix2);
                  } break;
                  
        case 'p': System.out.println("Please enter which matrix you want to use?(1/2): ");
              int choice5 = input.nextInt();
              if(choice5 == 1) {
              c.isPeriodic(Matrix1);;
              } 
              else if(choice5 == 2) {
              c.isPeriodic(Matrix2);
              } break;
        
        case 's': System.out.println("Please enter which matrix you want to use?(1/2): ");
                  int choice6 = input.nextInt();
                  if(choice6 == 1) {
                    System.out.println(c.symmetricORasymmetric(Matrix1));
                  }
                  else if(choice6 == 2) {
                    System.out.println(c.symmetricORasymmetric(Matrix2));
                  } break;
                  
        case 'o': System.out.println("Please enter which matrix you want to use?(1/2): ");
                  int choice7 = input.nextInt();
                  if(choice7 == 1) {
                    System.out.println(c.orthogonalORnot(Matrix1));
                  }
                  else if(choice7 == 2) {
                    System.out.println(c.orthogonalORnot(Matrix2));
                  } break;
                  
        default: System.out.println("Invalid operation!");
    }

    System.out.println("Do you want to continue(Yes/No): ");
    control = input.next();
  }

}

}

ASAĞIDAKİ KISIMLAR DA İŞLEMLERİN FONKSİYONU

class Operations { void sum(int[][] Matrix1, int[][] Matrix2) {

    int length = Matrix1.length;
    int sum[][] = new int[length][length];

    for(int i=0; i<length; i++) {
        for(int j=0; j<length; j++) {
            sum[i][j] = Matrix1[i][j] + Matrix2[i][j];
        }
    }
    for(int i=0; i<length; i++) {
        for(int j=0; j<length; j++) {
            System.out.printf("%4d",sum[i][j]);
    }
    System.out.println();
}

}

int sub(int[][] Matrix1, int[][] Matrix2) {
    int length = Matrix1.length;
    int sub[][] = new int[length][length];

    for(int i=0; i<length; i++) {
        for(int j=0; j<length; j++) {
            sub[i][j] = Matrix1[i][j] - Matrix2[i][j];
        }
    }
    for(int i=0; i<length; i++) {
        for(int j=0; j<length; j++) {
            System.out.printf("%4d",sub[i][j]);
    }
    System.out.println();
}
    return 0;

} static int mult(int[][] Matrix1, int[][] Matrix2) { int length = Matrix1.length; int mult[][] = new int[length][length];

    for (int i=0; i <length; i++) {
        for (int j=0; j <length; j++) {
            for (int k=0; k<length; k++) {
                mult[i][j] += Matrix1[i][k] * Matrix2[k][j];
            }
        }
    }
    for (int i=0; i <length; i++) {
        for (int j=0; j <length; j++) {
            System.out.printf("%8d",mult[i][j]);
        }   
        System.out.println(); 
}
    return 0;

}

void diagonalANDtrace(int[][] Matrix) { int length = Matrix.length; int diag[]=new int[length]; int trace = 0; for(int i=0;i<length;i++){ for(int j=0;j<length;j++){ if(i==j){ diag[i]=Matrix[i][j]; trace+=Matrix[i][j]; } } } System.out.println("DIAGONAL OF MATRIX :"); for(int i=0;i<length;i++){ System.out.printf("%3d",diag[i]);
} System.out.println(); System.out.println("TRACE OF MATRIX = "+trace); }

int isIdempotent(int[][] Matrix) { int length = Matrix.length; int idempotent_matrix[][]=new int[length][length]; System.out.println("IDEMPOTENT MATRIX : "); for(int i=0;i<length;i++){ for(int j=0;j<length;j++){ int sum=0; for(int k=0;k<length;k++){ sum+=Matrix[i][k]*Matrix[k][j]; } idempotent_matrix[i][j]= sum; } } for(int i=0;i<length;i++){ for(int j=0;j<length;j++){ System.out.printf("%3d",idempotent_matrix[i][j]); } System.out.println(); } boolean isidempotent=true; for(int i=0;i<length;i++){ for(int j=0;j<length;j++){ if(idempotent_matrix[i][j]!=Matrix[i][j]){ isidempotent=false; break; } } if(!(isidempotent)){ break; } } if(isidempotent){ System.out.println("Your matrix is an idempotent matrix"); }else{ System.out.println("Your matrix is not an idempotent matrix"); } return 0; }

static int isNilpotent(int[][] Matrix) { System.out.println("enter the power of matrix :"); Scanner get = new Scanner(System.in); int length = Matrix.length; int power=get.nextInt(); int nilpotent_matrix[][]=new int[length][length]; System.out.println("NILPOTENT MATRIX : "); for(int p=1;p<=power;p++){ for(int i=0;i<length;i++){ for(int j=0;j<length;j++){ int sum=0; for(int k=0;k<length;k++){

                sum+=Matrix[i][k]*Matrix[k][j];
            }
            nilpotent_matrix[i][j]+= sum;
        }
    }    
}

for(int i=0;i<length;i++){
    for(int j=0;j<length;j++){
        System.out.printf("%3d",nilpotent_matrix[i][j]);
    }
    System.out.println();
}
boolean isnilpotent=true;
for(int i=0;i<length;i++){
    for(int j=0;j<length;j++){
        if(nilpotent_matrix[i][j]!=0){
            isnilpotent=false;
            break;
        }
    }
    if(!(isnilpotent)){
        break;
    }
}
if(isnilpotent){
    System.out.println("Your matrix is a nilpotent matrix");
}else{
    System.out.println("Your matrix is not a nilpotent matrix");
}
return 0;

}

void isInvolitive(int[][] Matrix) { int length = Matrix.length; int involutive_matrix[][]=new int[length][length]; System.out.println("INVOLUTIVE MATRIX : "); for(int i=0;i<length;i++){ for(int j=0;j<length;j++){ int sum=0; for(int k=0;k<length;k++){ sum+=Matrix[i][k]*Matrix[k][j]; } involutive_matrix[i][j]= sum; } } for(int i=0;i<length;i++){ for(int j=0;j<length;j++){ System.out.printf("%3d",involutive_matrix[i][j]); } System.out.println(); } int unitmatrix[][]=new int[100][100]; for(int i=0;i<length;i++){ for(int j=0;j<length;j++){ if(i==j){ unitmatrix[i][j]=1; } } }

boolean isinvolutive=true;
for(int i=0;i<length;i++){
    for(int j=0;j<length;j++){
        if(involutive_matrix[i][j]!=unitmatrix[i][j]){
            isinvolutive=false;
            break;
        }
    }
    if(!(isinvolutive)){
        break;
    }
}
if(isinvolutive){
    System.out.println("Your matrix is an involutive matrix");
}else{
    System.out.println("Your matrix is not an involutive matrix");
}

}

int symmetricORasymmetric(int[][] Matrix) { int issymmetric=1; int isasymmetric=1; int length = Matrix.length;

System.out.println("TRANSPOSE OF MATRIX : ");
int transposematrix[][]=new int[length][length];

for(int i = 0; i < length; i++) {
    for(int j = 0; j < length; j++) {
    transposematrix[j][i]=Matrix[i][j];
    System.out.printf("%3d", Matrix[j][i]);
    }
System.out.println();
}
                    
for(int i = 0; i < length; i++) {
    for(int j = 0; j < length; j++) {
        if(transposematrix[i][j]!=Matrix[i][j]){
        issymmetric=0;
        break;
        }
    }
    if(issymmetric==0){
    break;
    }
}
                        
for(int i = 0; i < length; i++) {
    for(int j = 0; j < length; j++) {
        if((transposematrix[i][j])!=(-Matrix[i][j])){
        isasymmetric=0;
        break;
        }
    }
    if(isasymmetric==0){
    break;
    }
}
if(isasymmetric==1){
System.out.println("Your matrix is an asymmetric matrix .");
}else if(issymmetric==1){
System.out.println("Your matrix is a symmetric matrix .");
}
else{
System.out.println("Your matrix is neither symmetric nor asymmetric matrix .");
}

return 0;

}

static int orthogonalORnot(int[][] Matrix) { int length = Matrix.length; int tempMatrix[][] = new int[length][length]; int unitMatrix[][] = new int[length][length];

System.out.println("TRANSPOSE OF MATRIX: ");
int transposeMatrix[][] = new int[length][length];

for (int i = 0; i < length; i++) {
    for (int j = 0; j < length; j++) {
    transposeMatrix[j][i] = Matrix[i][j];
    System.out.printf("%3d", Matrix[j][i]);
    }
System.out.println();
}
        
for (int i = 0; i < length; i++) {
    for (int j = 0; j < length; j++) {
        tempMatrix[i][j] = Matrix[i][j] * transposeMatrix[i][j];
        if (i == j) {
            unitMatrix[i][j] = tempMatrix[i][j];
        }
    }
}
            
System.out.println("Transpose of Matrix * Matrix =");
for (int i = 0; i < length; i++) {
    for (int j = 0; j < length; j++) {
        System.out.printf("%3d", unitMatrix[i][j]);
    }
System.out.println();
}
            
boolean isUnitMatrix = true;
for (int i = 0; i < length; i++) {
    for (int j = 0; j < length; j++) {
        if ((i == j && unitMatrix[i][j] != 1) || (i != j && unitMatrix[i][j] != 0)) {
        isUnitMatrix = false;
        break;
        }
    }
    if (!isUnitMatrix) {
        break;
    }
}
if (isUnitMatrix) {
    System.out.println("Your matrix is an orthogonal matrix.");
} 
else {
    System.out.println("Your matrix is not an orthogonal matrix.");
}

return 0;

}

void isPeriodic(int[][] Matrix) { System.out.println("enter the period of matrix :"); Scanner get = new Scanner(System.in); int period=get.nextInt(); int length = Matrix.length; int periodic_matrix[][]=new int[length][length]; System.out.println("PERIODIC MATRIX : "); for(int p=1;p<=period+1;p++){ for(int i=0;i<length;i++){ for(int j=0;j<length;j++){ int sum=0; for(int k=0;k<length;k++){

                sum+=Matrix[i][k]*Matrix[k][j];
            }
            periodic_matrix[i][j]+= sum;
        }
    }    
}

for(int i=0;i<length;i++){
    for(int j=0;j<length;j++){
        System.out.printf("%3d",periodic_matrix[i][j]);
    }
    System.out.println();
}
boolean isperiodic=true;
for(int i=0;i<length;i++){
    for(int j=0;j<length;j++){
        if(periodic_matrix[i][j]!=Matrix[i][j]){
            isperiodic=false;
            break;
        }
    }
    if(!(isperiodic)){
        break;
    }
}
if(isperiodic){
    System.out.println("Your matrix is an periodic matrix");
}else{
    System.out.println("Your matrix is not an periodic matrix");
}

}