Course Content

Mathematics for Data Analysis and Modeling

## Mathematics for Data Analysis and Modeling

# Matrix Determinant

**The determinant** is a mathematical property of a **square matrix** (matrix with equal number of columns and rows) that provides valuable information about the matrix.
The determinant is denoted as **det(A)** or **|A|**, where A represents the matrix. The determinant is a single value that can be positive, negative, or zero.

The determinant carries several important properties and interpretations:

**Invertibility**: A square matrix A is invertible (non-singular) if and only if its determinant is nonzero;**Area or Volume Scaling**: For 2x2 and 3x3 matrices, the determinant provides information about the scaling factor or the change in area/volume under a linear transformation represented by the matrix;**Linear Independence**: The determinant can determine whether a set of vectors is linearly independent. If the determinant of a matrix composed of vectors is nonzero, the vectors are linearly independent;**Solution Existence**: In systems of linear equations represented by matrices, the determinant can determine whether a unique solution exists. If the determinant is nonzero, a unique solution exists; otherwise, there may be no solution or an infinite number of solutions.

In Python, we can calculate determinant using `np.linalg.det()`

method:

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