# pagemldivide

## Description

computes the left matrix divide of each page of N-D array `X`

= pagemldivide(`A`

,`B`

)`A`

into each
page of N-D array `B`

. Each page of the output array `X`

is given by `X(:,:,i) = A(:,:,i) \ B(:,:,i)`

. The pages of
`A`

and `B`

must be valid inputs to `mldivide`

(`\`

).

If `A`

and `B`

have more than three dimensions, then
all dimensions beyond the first two must have compatible sizes. `pagemldivide`

implicitly expands the extra
dimensions to divide all page combinations: ```
X(:,:,i,j,k) = A(:,:,i,j,k) \
B(:,:,i,j,k)
```

.

`[`

also returns the reciprocal condition number of each page of `X`

,`rcondA`

] = pagemldivide(___)`A`

, using any
of the input argument combinations in previous syntaxes. The value of
`rcondA(1,1,i)`

is the reciprocal condition number of
`A(:,:,i)`

. If `rcondA(1,1,i) < eps`

, then
`X(:,:,i) = A(:,:,i) \ B(:,:,i)`

returns a warning because the matrix is
ill conditioned. However, `pagemldivide`

does not issue a warning for
ill-conditioned inputs.

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

Results obtained using

`pagemldivide`

are numerically equivalent to computing the linear system solutions with each of the same matrices in a`for`

-loop. However, the two results might differ slightly due to floating-point round-off error.

## Algorithms

Similar to `mldivide`

, the `pagemldivide`

function
determines which algorithm to use in solving the linear systems in the input array by applying
a series of checks to the array pages. Different algorithms can be used with different pages
in the input array. `pagemldivide`

chooses between QR, Triangular, LU, and
Cholesky solvers for each array page in `A`

depending on its properties, as
shown in this diagram.

## Extended Capabilities

## Version History

**Introduced in R2022a**