# Matrix Operations

**Analysis with R**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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Matrix manipulation in R are very useful in Linear Algebra. Below are lists of common yet important functions in dealing operations with matrices:

- Transpose –
**t** - Multiplication –
**%*%** - Determinant –
**det** - Inverse –
**solve**, or**ginv**of MASS library - Eigenvalues and Eigenvectors –
**eigen**

Consider these matrices, $\left[\begin{array}{ccc}3&4&5\\2&1&3\\6&5&4\end{array}\right]$ and $\left[\begin{array}{ccc}6&7&5\\4&5&8\\7&6&6\end{array}\right]$. In R, these would be,

Transposing these, simply use **t**

Now multiplying these two matrices, that would be

For the determinant, we have

Taking the inverse of **matrix1** is achieved by **solve** or **ginv** R functions. Note that **ginv** is in MASS package,

And finally, for eigenvalues and eigenvectors simply use **eigen **

The output above returns the **$values**, which is the eigenvalues, and **$vectors**, the eigenvectors.

More about matrix here.

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