## COND Condition Number of a Matrix

### Usage

Calculates the condition number of a matrix. To compute the 2-norm condition number of a matrix (ratio of largest to smallest singular values), use the syntax
```   y = cond(A)
```

where A is a matrix. If you want to compute the condition number in a different norm (e.g., the 1-norm), use the second syntax

```   y = cond(A,p)
```

where `p` is the norm to use when computing the condition number. The following choices of `p` are supported

• `p = 1` returns the 1-norm, or the max column sum of A
• `p = 2` returns the 2-norm (largest singular value of A)
• `p = inf` returns the infinity norm, or the max row sum of A
• `p = 'fro'` returns the Frobenius-norm (vector Euclidean norm, or RMS value)

### Function Internals

The condition number is defined as

This equation is precisely how the condition number is computed for the case `p ~= 2`. For the `p=2` case, the condition number can be computed much more efficiently using the ratio of the largest and smallest singular values.

### Example

The condition number of this matrix is large
```--> A = [1,1;0,1e-15]

A =
1.0000    1.0000
0    0.0000

--> cond(A)

ans =
2000000000000000

--> cond(A,1)

ans =
2000000000000002
```

You can also (for the case `p=1` use `rcond` to calculate an estimate of the condition number

```--> 1/rcond(A)

ans =
2.0000e+15
```