# findLinearCombos

From caret v4.45
by Max Kuhn

##### Determine linear combinations in a matrix

Enumerate and resolve the linear combinations in a numeric matrix

- Keywords
- manip

##### Usage

`findLinearCombos(x)`

##### Arguments

- x
- a numeric matrix

##### Details

The QR decomposition is used to determine if the matrix is full rank and then identify the sets of columns that are involved in the dependencies.

To "resolve" them, columns are iteratively removed and the matrix rank is rechecked.

##### Value

- a list with elements:
linearCombos If there are linear combinations, this will be a list with elements for each dependency that contains vectors of column numbers. remove a list of column numbers that can be removed to counter the linear combinations

##### Examples

```
testData1 <- matrix(0, nrow=20, ncol=8)
testData1[,1] <- 1
testData1[,2] <- round(rnorm(20), 1)
testData1[,3] <- round(rnorm(20), 1)
testData1[,4] <- round(rnorm(20), 1)
testData1[,5] <- 0.5 * testData1[,2] - 0.25 * testData1[,3] - 0.25 * testData1[,4]
testData1[1:4,6] <- 1
testData1[5:10,7] <- 1
testData1[11:20,8] <- 1
findLinearCombos(testData1)
testData2 <- matrix(0, nrow=6, ncol=6)
testData2[,1] <- c(1, 1, 1, 1, 1, 1)
testData2[,2] <- c(1, 1, 1, 0, 0, 0)
testData2[,3] <- c(0, 0, 0, 1, 1, 1)
testData2[,4] <- c(1, 0, 0, 1, 0, 0)
testData2[,5] <- c(0, 1, 0, 0, 1, 0)
testData2[,6] <- c(0, 0, 1, 0, 0, 1)
findLinearCombos(testData2)
```

*Documentation reproduced from package caret, version 4.45, License: GPL-2*

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