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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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