The inertia command computes the inertia of a real symmetric matrix, i.e. the number of positive, negative and zero eigenvalues, by performing LDL decomposition (see Section 5.49.9). It can also use the factorization for solving a system of linear equations if certain inertia-related conditions are satisfied.
⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |
⎡ ⎣ | 2,1,0 | ⎤ ⎦ |
⎡ ⎣ | 2,1,0 | ⎤ ⎦ | , | ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ |
⎡ ⎣ | 2,1,0 | ⎤ ⎦ | , | ⎡ ⎣ | ⎤ ⎦ |