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@jemoka / Jemoka Knowledge Base / raw/concept/kbhdeterminants.md
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--- title: "determinants" source: https://www.jemoka.com/posts/kbhdeterminants/ --- For a matrix, for instance, like: \begin{equation} \begin{bmatrix} a & b \\ c & d \end{bmatrix} \end{equation} We wish to find the matrix’s determinant; we write it down as: \begin{equation} \begin{vmatrix} a & b \\ c & d \end{vmatrix} \end{equation} geometric interpretation of determinants Geometrically, determinants are how matrices send a unit object after its mapping; i.e. how does it transform the area of a unit square. determinants can be computed along any axes You can pick any row or column as the “axes”, and expand the matrix along any direction