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You've got questions? Maybe here you'll find answers.
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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