Matrix multiplication by matrix transposed in C language

Question

I am new to programming and I am trying to make a program in C language that multiplies a 3x3 matrix by transposing it and prints the result. I’m having a hard time creating a multiplication algorithm between the matrix and the transposta. Any help will be willingly.

Follows the code:

used libraries (stdio.h and stdlib.h)

int main(){

int mat[3][3], mat_transposta[3][3], mat_resultado[3][3];
int i, j;

// leitura matriz
for(i = 0; i < 3; i++){
    for(j = 0; j < 3; j++){
        scanf("%d",&mat[i][j]);
    }
    for(i = 0; i < 3; i++){
        for(j = 0; j < 3; j++){
            mat_transposta[i][j] = mat[j][i]; // transformação matriz principal p/ transposta (FUNCIONANDO)
        }
    }
        for(i = 0; i < 3; i++){
            for(j = 0; j < 3; j++){
                mat[i][j] *= mat_transposta[i][j];// multiplicação da matriz pela sua transposta correspondente

            }
        }

            for (i = 0; i < 3; i++){
                for (j = 0; j < 3; j++){
                    printf("%d\t", mat_resultado[i][j]); // impressão matriz resultado (A SAÍDA TEM QUE SER NESSE FORMATO)
                }
                printf("\n");
            }
return 0;
}

So the X of the question is to solve the following algorithm (that is logically wrong, I know). I could not create a pattern ( i and j) for multiplication, which could be implemented as the minimum use of commands for to perform this multiplication.

for(i = 0; i < 3; i++){
            for(j = 0; j < 3; j++){
                mat[i][j] *= mat_transposta[i][j];// multiplicação da matriz pela sua transposta correspondente

            }
        }

I know that in the first multiplication of line 1 by transposta **i0j0*i0j0 + i0j1*i1j0 + i0j2*i2j0** and in the second multiplication of line 1 by transpose **i0j0*i0j1 + i0j1*i1j1 + i0j2*i2j1** and in the third multiplication of line 1 by transpose **i0j0*i0j2 + i0j1*i1j2 + i0j2*i2j2**

and then in the first multiplication of line 2 by transpose **i1j0*i0j0 + i1j1*i1j0 + i1j2*i2j0** in the second multiplication of line 2 by transpose **i1j0*i0j1 + i1j1*i1j1 + i1j2*i2j1** in the third multiplication of line 2 by transpose **i1j0*i0j2 + i1j1*i1j2 + i1j2*i2j2**

and finally in the first multiplication of line 3 by transpose **i2j0*i0j0 + i2j1*i1j0 + i2j2*i2j0** in the second multiplication of line 3 by transpose **i2j0*i0j1 + i2j1*i1j1 + i2j2*i2j1** in the 3rd multiplication of line 3 by transpose **i2j0*i0j2 + i2j1*i1j2 + i2j2*i2j2**

An example, if the matrix (mat[i][j]) entered by the user for 10, 0, 1, 3, 5, 2, -4, 2, 3. The result matrix (mat_resultado) will have at output the following numbers: 101, 32, -37, 32, 38, 4, -37, 4, 29.

Answer 1

First of all the product of two matrices is defined only when the number of columns of the first matrix is equal to the number of rows of the second matrix.

#define L 3
#define M 4
...
    int mat[L][M], mat_transposta[M][L], mat_resultado[L][L];
    int i, j, k;
    ...
    /* Multiplicação*/
    for (i=0; i<L; i++) {
        for (j=0; j<L; j++) {
            mat_resultado[i][j] = 0;
            for (k=0; k<M; k++) {
                mat_resultado[i][j] += mat[i][k] * mat_transposta[k][j];
            }
        }
    }
    ...

In your particular case L and M must have the same value, ie 3.

===================

Give a studied in the product definition of matrices to understand the use of the variable k and its loop.