What are matricies

Rules of mathematical actions with matrices allow them to be widely applied to write systems of equations. At the same time, the equations themselves are written in the rows of the matrix, and the unknowns in the columns. Thus, the solution of a system of equations is reduced to performing operations with the matrix.

Matrices can be folded and subtracted, provided that all of the matrices are of the same size. In addition, they can be multiplied in several ways. The first way is to multiply a matrix with a certain number of columns to the right by a matrix with the same number of rows. The second way is to multiply by the vector matrix, provided that this vector is treated as a separate case of the matrix. The third way is to multiply the matrix by a scalar magnitude. For the

first time, matrices began to apply mathematicians of ancient China to solve linear equ At the same time, the matrices began to use Arabic mathematicians, who developed principles and rules of addition for them. However, the term “matrix” itself was introduced only in 1850g. Before that, they were called “magic squares”.

Matrices are denoted by capital letters A:mxn, where A is the name of the matrix, M is the number of rows in the matrix, and N is the number of columns. Items — corresponding lowercase letters with indices indicating their number in row and column a (m, n).

Rectangular shape matrices are most common, although in the distant past mathematicians considered triangular as well. If the number of rows and columns of a matrix is the same, it is called square. In this case, M=N already has the name of the order of the matrix. A matrix with only one row is referred to as a string. A matrix with just one column is called a column. A diagonal matrix is a square matrix in which only elements arranged diagonally are not zero. If all elements are equal to one, the matrix is called unit if zero is zero.

If you change rows and columns in the matrix, it becomes transposed. If you replace all elements with complex conjugate, it becomes complex conjugate. In addition, there are other kinds of matrices determined by conditions that are superimposed on matrix elements. But most such conditions apply only to square matrices.

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