Scilab 6.0.1

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# projspec

spectral operators

### Syntax

[S,P,D,i]=projspec(A)

### Arguments

- A
square matrix

- S, P, D
square matrices

- i
integer (index of the zero eigenvalue of

`A`

).

### Description

Spectral characteristics of `A`

at 0.

`S`

= reduced resolvent at 0 (`S`

= -Drazin_inverse(`A`

)).

`P`

= spectral projection at 0.

`D`

= nilpotent operator at 0.

`index`

= index of the 0 eigenvalue.

One has `(s*eye()-A)^(-1) = D^(i-1)/s^i +... + D/s^2 + P/s - S - s*S^2 -...`

around the singularity s=0.

### Examples

### See also

- coff — resolvent (cofactor method)

## Comments

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