Keywords [1] An eigenvector \(x\) lies along the same line as \(Ax\): \(Ax=\lambda x\). The eigenvalue is \(\lambda\). [2] If \(Ax=\lambda x\), then \(A^2x=\lambda^2x\) and \(A^{-1}x=\lambda^...

Introduction Object detection task has become mature with excellent performance. Detecting a person and a cup of coffee is now a relatively easy task. However, what if the person is holding th...

Keywords [1] \(A^{-1} = \frac{C^T}{det(A)}\). Then, \((A^{-1})\_{ij}=\) cofactor \(C\_{ji}\) divided by the determinant of \(A\) [2] Cramer’s Rule computes \(x=A^{-1}b\) from \(x_j=det(A\ \te...

Keywords [1] 2 by 2: \(ad-bc\) has \(2!\) terms with \(\pm\) signs. n by n: \(det(A)\) adds n! terms with \(\pm\) signs. [2] For \(n=3\), \(det(A)\) adds \(3!=6\) terms. Two terms are \(+a_{1...

Keywords [1] The determinant of \(A = \begin{bmatrix} a & b \\\ c & d \end{bmatrix}\) is \(ad-bc\). Singular matrix \(A = \begin{bmatrix} a & xa \\\ c & xc \end{bmatrix}\) has ...

Triple Integrals If \(f\) is continuous on the rectangular box \(B = [a,b] \times [c,d] \times [r,s]\), then [\iiint_B f(x,y,z)dV = \int_r^s \int_c^d \int_a^b f(x,y,z)dxdydz] ...

Surface Area stewart-calculus-8th-edition The surface of \(S\) is defined as [A(S) = \lim{m,n \rightarrow \infty} \sum{i=1}^m \sum{j=1}^n \Delt...

Double Integrals in Polar Coordinates stewart-calculus-8th-edition Suppose we want to evaluate a double integral \(\iint_Rf(x,y)dA\) but it’s qu...

Double Integral of \(f\) over \(D\) stewart-calculus-8th-edition Often we want to evaluate integrals not just over rectangles but also over gene...

Introduction https://herbwood.tistory.com/17 YOLO (You Only Look Once) object detection model has been increasingly popular especially due to it...