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See the recommended documentation of this function

Scilab help >> Linear Algebra > rank

# rank

rank

### Calling Sequence

```[i]=rank(X)
[i]=rank(X,tol)```

### Arguments

X

real or complex matrix

tol

nonnegative real number

### Description

`rank(X)` is the numerical rank of `X` i.e. the number of singular values of X that are larger than `norm(size(X),'inf') * norm(X) * %eps`.

`rank(X,tol)` is the number of singular values of `X` that are larger than `tol`.

Note that the default value of `tol` is proportional to `norm(X)`. As a consequence `rank([1.d-80,0;0,1.d-80])` is 2 !.

### Examples

```rank([1.d-80,0;0,1.d-80])
rank([1,0;0,1.d-80])```

• svd — singular value decomposition
• qr — QR decomposition
• rowcomp — row compression, range
• colcomp — column compression, kernel, nullspace
• lu — LU factorization with pivoting

 << range Linear Algebra rankqr >>

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