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# balanc

matrix or pencil balancing

### Syntax

[Ab,X]=balanc(A) [Eb,Ab,X,Y]=balanc(E,A)

### Arguments

- A:
a real square matrix

- X:
a real square invertible matrix

- E:
a real square matrix (same dimension as

`A`

)- Y:
a real square invertible matrix.

### Description

Balance a square matrix to improve its condition number.

`[Ab,X] = balanc(A)`

finds a similarity transformation
`X`

such that

`Ab = inv(X)*A*X`

has approximately equal row and column norms.

For matrix pencils,balancing is done for improving the generalized eigenvalue problem.

`[Eb,Ab,X,Y] = balanc(E,A)`

returns left and right transformations `X`

and `Y`

such that `Eb=inv(X)*E*Y, Ab=inv(X)*A*Y`

### Remark

Balancing is made in the functions `bdiag`

and `spec`

.

## Comments

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