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See the recommended documentation of this function

# norm

matrix norm

### Syntax

`[y]=norm(x [,flag])`

### Arguments

x

real or complex vector or matrix (full or sparse storage)

flag

string (type of norm) (default value =2)

y

norm

### Description

For matrices

norm(x)

or `norm(x,2)` is the largest singular value of `x` (`max(svd(x))`).

norm(x,1)

The l_1 norm `x` (the largest column sum : `max(sum(abs(x),'r'))` ).

norm(x,'inf'),norm(x,%inf)

The infinity norm of `x` (the largest row sum : `max(sum(abs(x),'c'))` ).

norm(x,'fro')

Frobenius norm i.e. `sqrt(sum(diag(x'*x)))`.

For vectors

norm(v,p)

The l_p norm (`sum(v(i)^p))^(1/p)` .

norm(v), norm(v,2)

The l_2 norm

norm(v,'inf')

`max(abs(v(i)))`.

### Examples

```A=[1,2,3];
norm(A,1)
norm(A,'inf')
A=[1,2;3,4]
max(svd(A))-norm(A)

A=sparse([1 0 0 33 -1])
norm(A)```

### See also

• h_norm — H-infinity norm
• dhnorm — discrete H-infinity norm
• h2norm — H2 norm of a continuous time proper dynamical system
• abs — absolute value, magnitude
• svd — singular value decomposition

### Comments

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