# PrincipalComponents

PrincipalComponents[matrix]

transforms elements of matrix into unscaled principal components.

# Details and Options

• PrincipalComponents gives the principal component transform of matrix.
• The principal components of matrix are linear transformations of the original columns into uncorrelated columns arranged in order of decreasing variance.
• PrincipalComponents supports a Method option. The following explicit settings can be specified:
•  "Covariance" uses covariance method (default) "Correlation" uses correlation method
• If principal components of scaled columns (standardized principal components) are required, the option Method"Correlation" should be used.
• The dimensions of PrincipalComponents[matrix] are the same as the dimensions of matrix.
• If matrix consists of exact numbers or symbols, the result is also exact or symbolic, respectively.

# Examples

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## Basic Examples(1)

Principal components of two datasets, treated as the columns of a matrix:

## Scope(3)

Principal components computed with arbitrary-precision numbers:

Principal components of exact numbers:

Principal components computation involving symbolic expressions:

## Options(1)

### Method(1)

Principal components using correlation scaling:

## Properties & Relations(2)

The principal component columns are ordered by decreasing variance:

The mean of each principal component column is zero:

The principal component columns are not correlated:

The setting Method->"Correlation" yields the same results as standardizing the input matrix:

## Possible Issues(1)

For certain symbolic matrices the result may be very large:

## Neat Examples(1)

Align the principal axis of a two-dimensional shape with the horizontal axis:

Wolfram Research (2010), PrincipalComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/PrincipalComponents.html.

#### Text

Wolfram Research (2010), PrincipalComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/PrincipalComponents.html.

#### CMS

Wolfram Language. 2010. "PrincipalComponents." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PrincipalComponents.html.

#### APA

Wolfram Language. (2010). PrincipalComponents. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PrincipalComponents.html

#### BibTeX

@misc{reference.wolfram_2024_principalcomponents, author="Wolfram Research", title="{PrincipalComponents}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PrincipalComponents.html}", note=[Accessed: 18-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_principalcomponents, organization={Wolfram Research}, title={PrincipalComponents}, year={2010}, url={https://reference.wolfram.com/language/ref/PrincipalComponents.html}, note=[Accessed: 18-July-2024 ]}