CAex {Matrix} | R Documentation |

## Albers' example Matrix with "Difficult" Eigen Factorization

### Description

An example of a sparse matrix for which `eigen()`

seemed
to be difficult, an unscaled version of this has been posted to the
web, accompanying an E-mail to R-help
(https://stat.ethz.ch/mailman/listinfo/r-help), by
Casper J Albers, Open University, UK.

### Usage

`data(CAex)`

### Format

This is a `72 \times 72`

symmetric matrix with 216
non-zero entries in five bands, stored as sparse matrix of class
`dgCMatrix`

.

### Details

Historical note (2006-03-30):
In earlier versions of **R**, `eigen(CAex)`

fell into an
infinite loop whereas `eigen(CAex, EISPACK=TRUE)`

had been okay.

### Examples

```
data(CAex)
str(CAex) # of class "dgCMatrix"
image(CAex)# -> it's a simple band matrix with 5 bands
## and the eigen values are basically 1 (42 times) and 0 (30 x):
zapsmall(ev <- eigen(CAex, only.values=TRUE)$values)
## i.e., the matrix is symmetric, hence
sCA <- as(CAex, "symmetricMatrix")
## and
stopifnot(class(sCA) == "dsCMatrix",
as(sCA, "matrix") == as(CAex, "matrix"))
```

[Package

*Matrix* version 1.5-1

Index]