HIGHER ALGEBRA.
DETERMINANTS AND MATRICES & IMPORTANT NOTES.
§1. The concept of a numerical Matrix. General information about the types
of Matrix
~MATRİX~
The theory of Matrices and determinants is widely used to solve and
investigate systems of linear equations. Therefore, it is necessary to provide
information about matrices. A matrix is a rectangular array of numbers,
symbols, or expressions arranged in rows and columns.
and are matrices.
The numbers that make up the table and are denoted as aij are called the
elements of the Matrix. The elements arranged horizontally in the table
form the i number of rows of this matrix, and the elements arranged
vertically form its j number of columns. Binary indices used to distinguish
matrix elements from each other indicate the location of the element in the
table.Thus, the first index indicates the row in which the element is located,
and the second index indicates the column number in which the element is
located. For example, based on the indices of the element denoted by a24, it
can be said that this element is located at the intersection of the second row
and the fourth column of the matrix. Thus, aij is understood as an element
of the matrix that stands at the intersection of an arbitrary i -numbered row
and an arbitrary j -numbered column. If an arbitrary element of the Matrix
, consisting of rows m and n columns is aij, then the values of the indices i
and j are as follows: i =1,..., m and j = 1,..., n
In short, sometimes the matrix is denoted as
or
or
.
In general, the matrix is formed by one letter, for example: A, B,C it is
denoted by. For simplicity, it is possible to use
or
.
A matrix with the number of rows m and the number of columns n is called
a rectangular matrix of size mn , when in the special case n=m, it’s
called square matrix of order n.
DETERMINANTS AND MATRICES & IMPORTANT NOTES.
§1. The concept of a numerical Matrix. General information about the types
of Matrix
~MATRİX~
The theory of Matrices and determinants is widely used to solve and
investigate systems of linear equations. Therefore, it is necessary to provide
information about matrices. A matrix is a rectangular array of numbers,
symbols, or expressions arranged in rows and columns.
and are matrices.
The numbers that make up the table and are denoted as aij are called the
elements of the Matrix. The elements arranged horizontally in the table
form the i number of rows of this matrix, and the elements arranged
vertically form its j number of columns. Binary indices used to distinguish
matrix elements from each other indicate the location of the element in the
table.Thus, the first index indicates the row in which the element is located,
and the second index indicates the column number in which the element is
located. For example, based on the indices of the element denoted by a24, it
can be said that this element is located at the intersection of the second row
and the fourth column of the matrix. Thus, aij is understood as an element
of the matrix that stands at the intersection of an arbitrary i -numbered row
and an arbitrary j -numbered column. If an arbitrary element of the Matrix
, consisting of rows m and n columns is aij, then the values of the indices i
and j are as follows: i =1,..., m and j = 1,..., n
In short, sometimes the matrix is denoted as
or
or
.
In general, the matrix is formed by one letter, for example: A, B,C it is
denoted by. For simplicity, it is possible to use
or
.
A matrix with the number of rows m and the number of columns n is called
a rectangular matrix of size mn , when in the special case n=m, it’s
called square matrix of order n.
