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Scilab Help >> Linear Algebra > proj

# proj

projection

### Syntax

`P = proj(X1,X2)`

### Arguments

X1,X2

two real matrices with equal number of columns

P

real projection matrix (`P^2=P`)

### Description

`P` is the projection on `X2` parallel to `X1`.

### Examples

```X1=rand(5,2);X2=rand(5,3);
P=proj(X1,X2);
norm(P^2-P,1)
trace(P)    // This is dim(X2)
[Q,M]=fullrf(P);
svd([Q,X2])   // span(Q) = span(X2)```

### See also

• projspec — spectral operators
• orth — orthogonal basis
• orthProj — Computes the orthogonal projection of a point to a polyline in the plane.
• fullrf — full rank factorization

### Comments

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