Matrix QR decomposition is very useful in least square fitting model. But there is no function available to do it in OpenCV directly. So i write a function to do it myself. It is based on the House Holder Algorithm. The defailed algorithm can be foun…
一.算法原理 请参考我在大学时写的<QR方法求矩阵全部特征值>,其包含原理.实例及C语言实现:http://www.docin.com/p-114587383.html 二.源码分析 这里有一篇文章<使用MapRedece进行QR分解的步骤>可以看看 /** For an <tt>m x n</tt> matrix <tt>A</tt> with <tt>m >= n</tt>, the QR decom…
I find it may cost me so much time in doing such solutions to exercises and problems....I am sorry that I could not be persistent in doing it...Wish I could just recover it later on. [Bhatia.Matrix Analysis.Solutions to Exercises and Problems]PrI.6.1…
Show that the following statements are equivalent: (1). $A$ is positive. (2). $A=B^*B$ for some $B$. (3). $A=T^*T$ for some upper triangular $T$. (4). $A=T^*T$ for some upper triangular $T$ with nonnegative diagonal entries. If $A$ is positive defini…
Use the QR decomposition to prove Hadamard's inequality: if $X=(x_1,\cdots,x_n)$, then $$\bex |\det X|\leq \prod_{j=1}^n \sen{x_j}. \eex$$ Equality holds here if and only if the $x_j$ are mutually orthogonal or some $x_j$ are zero. 解答: $$\beex \bea |…
