03_002_Trace_of_matrix_Determinant_value_of_matrix.html ========================================================= Trace of matrix above characteristics are importantly used when finding solution on eigenvalue question ========================================================= determinant value of matrix matrix has many elements To inform matrix, you should inform all of elements of matrix, which is complex way So, what if you can inform one value which expresses unique characteristic of matrix? determinant value of matrix is one real number which expresses matrix determinant of matrix $$$A = |A| = \sum\limits_{k=1}^{d} a_{ik}|A_{ik}|(-1)^{k+i}$$$ $$$A_{ik}$$$ : sub-matrix of A, which you remove ith row, kth column from matrix A ========================================================= determinant is only defined in squre matrix $$$|A|=|A^{T}|$$$ ========================================================= determinant of 2x2 matrix A : $$$|A| = \begin{vmatrix} a_{11}&a_{12}\\a_{21}&a_{22} \end{vmatrix} = a_{11}&a_{22} - a_{12}&a_{21}$$$ determinant of 3x3 matrix A : uses computer