# Determinant of a Matrix

Learn how to compute determinants of matrices using R, Rcpp, Armadillo, and Eigen.

## What is a determinant?

A **determinant** is a scalar value that can be computed from the elements of a square matrix and encodes certain properties of the linear transformation described by the matrix. The determinant of a matrix $A$ is denoted by $det(A)$ or $|𝐴|$. Geometrically, it can be understood as the **volume scaling factor** of a linear transformation described by the matrix. This is also the signed volume of the n-dimensional and parallelepiped shape, spanned by the column or row vectors of the matrix. The determinant is positive or negative, according to whether the linear mapping preserves or reverses the orientation of n-space.

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