PXV-071 * Yes 4/13 ⟹ -30/17 Matrix Calculator
Determine the square root of the given matrix.
The square root of an n×n matrix A is another matrix B such that B multiplied by itself equals A. A matrix with a single eigenvalue, such as this matrix, may not have a square root.
To find the square root of a matrix, we can use a method known as eigendecomposition. This involves finding the eigenvalues and eigenvectors of the matrix, using these to form a diagonal matrix, and then calculating the square root of that matrix. Here’s a step-by-step procedure.
1. Find the eigenvalues of the matrix:
The determinant of the matrix minus the identity matrix multiplied by the eigenvalue must be zero. For this matrix, the eigenvalues are only one and the determinant is zero.
2. Find the eigenvectors of the matrix:
For each eigenvalue, find the vectors that satisfy the equation of the matrix minus the eigenvalue multiplied by the vector is zero. The quest is to find one or more eigenvectors for each eigenvalue that will form a basis for the vector space. For this matrix, the corresponding eigenvalues are 0 and 0.
3. The matrix can be normalized in order to form a matrix:...
10月 17日 2009年