Matrix is a mathematical concept, a rectangular array of numbers, usually expressed in square brackets or parentheses. Matrix is one of the basic concepts in linear algebra, which is widely used in computer science, physics, engineering and other fields.
Matrix can be regarded as a mathematical object, which consists of a set of numbers arranged in a rectangle according to certain rules. For example, a matrix with 2 rows and 3 columns can be expressed as: where each number can be expressed by a subscript, for example, the number in the first row and the second column is 2, which can be written as A. This way of expressing elements in the matrix by subscripts is sometimes called "matrix index".
Definition of matrix:
1, complex matrix:
The elements in a matrix can be real numbers or complex numbers. If all the elements in a matrix are complex numbers, then the matrix is called a complex matrix.
2. Matrix addition:
For two matrices A and B with the same size, their sum is defined as a new matrix C, where C[i, j]=A[i, j]+B[i, j].
3. Matrix multiplication:
For two matrices A and B, their product is defined as a new matrix C, where C[i, j]=∑(A[i, k]*B[k, j]), where the value range of k is from 1 to the number of columns in A or the number of rows in B. ..
4, matrix transpose:
For a matrix A, its transposition is defined as a new matrix B, where B[i, j]=A[j, i]. In other words, the number of rows of B is equal to the number of columns of A, and the number of columns of B is equal to the number of rows of A. ..
Application of matrix:
In addition to the above basic concepts, matrices have many other applications and extensions. For example, matrices can be used to represent linear equations, image processing and computer graphics, data mining and machine learning. Matrix is a very important mathematical concept, which is widely used in various fields. Mastering the basic concepts and operations of matrices is very helpful for understanding and applying knowledge in related fields.