Let A=(aij) be an n-order square matrix, and the sum of diagonal elements of A is called the trace of A, and denoted as trA, that is, TRA = A1+A22+ANN.
The eigenvalue of a is α t β = 3,0,0,0.
Because aα = (α β T) α = α (β T α) = (β T α) α.
So α is the eigenvector of A with the eigenvalue β tα = 3.
Because r(A)= 1.
Therefore, the basic solution system of homogeneous linear equations Ax=0 contains n- 1 vectors.
matrix
It is a common tool in applied mathematics disciplines such as advanced algebra and statistical analysis. In physics, matrices have applications in circuit science, mechanics, optics and quantum physics. In computer science, three-dimensional animation also needs matrix. Matrix operation is an important problem in the field of numerical analysis. Decomposition of a matrix into a combination of simple matrices can simplify the operation of the matrix in theory and practical application.