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Matrix is like a two-dimensional array of numbers.
A(i,j) means the number in the matrix A in the i-th row and j-th column.
Here goes the short explanation of operations.

  • +x,*x - operations with numbers. This is simple. Number x added to every number in matrix or every number in matrix is multiplied by x.
  • +M - operations with another matrix. This is also simple. If A and B are both matrices of m rows and n columns, then to every number in matrix A will be added appropriate number of matrix B, i.e. A(i,j)=A(i,j)+B(i,j).
  • *M - multiplication of matrices. The number of columns of the first matrix must be equal to the number of rows in the second matrix for this operation to be valid. If matrix A contains m rows and n columns, and matrix B contains n rows and k columns, then the result matrix will be of m rows and k columns and its element in the i-th row and the j-th column is a scalar product of the i-th row of the matrix A and the j-th column of the matrix B.
  • det - calculates square matrix's determinant. Determinant is a number calculated from the matrix's content according to a clever algorithm. What algorithm? This is difficult to explain, I cannot put it short. Try searching inet.
  • inverse - invertes matrix. Also applies to square matrices only. Inverse matrix is build in such a way that, if multiplied by the origin matrix, gives E-matrix ( A*B=B*A=E, where B is inverse for A). E-matrix contains all zeroes but E(i,i)=1.
  • trans - transponate matrix. Elements A(i,j) and A(j,i) are swapped.
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