Orthostochastic matrix — doubly stochastic matrix whose entries are the squares of the absolute values of the entries of some orthogonal matrix; Precision matrix — a symmetric n×n matrix, formed by inverting the covariance matrix. The matrix $\hat{\mathbf {R}}_{n}$ is a popular object in multivariate analysis and it has many connections to other problems. (This one has 2 Rows and 2 Columns) The determinant of that matrix is (calculations are explained later): 3×6 − 8×4 = 18 − 32 = −14. The determinant is linear in each row separately. a33. det(abcd)=a det(d)−b det(c)=ad−bc. Matrix Determinants (2 of 3: The Determinant's Geometric Meaning) - Duration: 10:35. Unfortunately, these calculations can get quite tedious; already for 3×33 \times 33×3 matrices, the formula is too long to memorize in practice. The determinant of a matrix is a special number that can be calculated from a square matrix. In the case of a 2×22 \times 22×2 matrix, the determinant is calculated by. A=(123456789)  ⟹  A11=(5689).A = \begin{pmatrix}1&2&3\\4&5&6\\7&8&9\end{pmatrix} \implies A_{11} = \begin{pmatrix}5&6\\8&9\end{pmatrix}.A=⎝⎛​147​258​369​⎠⎞​⟹A11​=(58​69​). Without doing the calculation nor telling you the formula, the area would be 1. (10−19110−6−19110013−8013000970000−5).\left(\begin{array}{cc}1&0&-1&9&11\\0&-6&-1&9&11\\0&0&\frac{1}{3}&-80&\frac{1}{3}\\0&0&0&9&7\\0&0&0&0&-5 \end{array}\right).⎝⎜⎜⎜⎜⎛​10000​0−6000​−1−131​00​99−8090​111131​7−5​⎠⎟⎟⎟⎟⎞​. Hat matrix — a square matrix used in statistics to relate fitted values to observed values. Matrices do not have definite value, but determinants have definite value. The recursive step is as follows: denote by AijA_{ij}Aij​ the matrix formed by deleting the ithi^\text{th}ith row and jthj^\text{th}jth column. The first has positive sign (as it has 0 transpositions) and the second has negative sign (as it has 1 transposition), so the determinant is. Let’s now study about the determinant of a matrix. {\displaystyle \det(V)=\prod _{1\leq i