f

#### How much do we know about A after a few eigenvalues known?

```Hi,

I have such a question about a system:

x_(t+1)=3DA*x_t+w_t

w_t is Gaussian noise.

x_t is a R^6 column vector.

The eigenvalues of A are:

0.9973=C2=B10.0730j,  0.9995=C2=B10.0324j,   0.9941=C2=B10.1081j

I wonder what A could be.

Regards,
```
 0
fl
12/25/2016 12:38:08 AM
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```On Saturday, December 24, 2016 at 7:38:13 PM UTC-5, fl wrote:
> Hi,
>=20
> I have such a question about a system:
>=20
> x_(t+1)=3DA*x_t+w_t
>=20
>=20
> w_t is Gaussian noise.
>=20
> x_t is a R^6 column vector.
>=20
>=20
> The eigenvalues of A are:
>=20
> 0.9973=C2=B10.0730j,  0.9995=C2=B10.0324j,   0.9941=C2=B10.1081j
>=20
>=20
> I wonder what A could be.
>=20
>=20
>=20
>=20
> Regards,

I find an equation used A in this way:

Sigma_(t+1)=3DA*Sigma_t*A^T+W

W is the co-variance matrix of w_t
Sigma is the co-variance of x_t.

After ignoring 0 eigenvalues, we can solve Sigma (if Sigma_(t+1)=20
converges to Sigma_t), and if we know W?

Thanks,

```
 0
fl
12/25/2016 12:45:47 AM