# Reciprocal Condition

Compute reciprocal condition of square matrix in 1-norm

Libraries:
DSP System Toolbox / Math Functions / Matrices and Linear Algebra / Matrix Operations

## Description

The Reciprocal Condition block computes the reciprocal of the condition number for a square input matrix A.

Here is the equivalent MATLAB® code.

`y = rcond(A) `

or

`$y=\frac{1}{\kappa }=\frac{1}{{‖{A}^{-1}‖}_{1}{‖{A}^{}‖}_{1}},$`

where κ is the condition number (κ ≥ 1), and y is the scalar output (0 ≤ y < 1).

The matrix 1-norm, ${‖A‖}_{1}$, is the maximum column-sum in the M-by-M matrix A.

`${‖A‖}_{1}=\stackrel{\mathrm{max}}{1\le j\le M}\sum _{i=1}^{M}|{a}_{ij}|$`

For a 3-by-3 matrix:

## Ports

### Input

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Specify the input matrix as a square matrix.

Data Types: `single` | `double`

### Output

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Reciprocal of the condition number for a square input matrix A, returned as a scalar.

If input is well conditioned, the output is near 1.0. If input is badly conditioned, the output is near 0.0.

Data Types: `single` | `double`

## Block Characteristics

 Data Types `double` | `single` Direct Feedthrough `no` Multidimensional Signals `no` Variable-Size Signals `no` Zero-Crossing Detection `no`

## References

[1] Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.

## Version History

Introduced before R2006a