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A: Write your matrix as $A = \begin{bmatrix} A_1 & \dots & A_j &\dots &A_n\end{bmatrix}$, where the $A_i$ are $m\times m$ submatrices. Consider the $m\times n$ matrix $D=\begin{bmatrix}A_1\\\vdots\\ A_j\\ \mathbf{e}_m\end{bmatrix}$, where $\mathbf{e}_m$ is the vector with all entries $1$ (of size $m\times 1$). Then $\text{rank}(A+I_n) = \text{rank}(D+I_m) = \text{rank}(D) +m$, since the rowspace of $D$ is the same as that of $A+I_n$. Likewise, if we write $B=\begin{bmatrix}A_1\\\vdots\\ A_j\\ -\mathbf{e}_m\end{bmatrix}$, we have $\text{rank}(A-I_n) = \text{rank}(B-I_m) = \text{rank}(B) +m$. Generally, if you want to find the rank of a matrix of size $m\times n$, it is often easier to write it as a block matrix $C$ where the last $m-n$ columns are identically zero and then compute the rank of $C-I_m$. Microcluster 1 from the upcoming DC Movie Aquaman will be a new Batman Aquaman (2018) will be another solid origin story for the Justice League, and according to Comicbook.com, we could see some Batman in this origin in the form of a defeated Batman. That will be the Microcluster, a mini-superhero that’ What's New in the Photoshop 2021 (Version 22.4.1)? Q: Angular Material data-binding not working I am trying to create a simple Angular application which has 2 controllers: app.controller('MainCtrl', function($scope, $http) { $scope.name = "World"; $scope.body = "Hello, I'm main controller"; }); app.controller('DetailCtrl', function($scope, $http) { $scope.body = $scope.name; }); This is the html: {{name}} {{body}} {{body}} However, on the browser console I can see in both cases body = undefined. What am I missing here? Thanks! A: Also see this answer, for example: The typescript compiler introduces a simple name collision in the syntax for controller declaration. A TypeScript class that uses a property name that matches a method declared in another controller will not work, for example: app.controller('mainCtrl', function($scope) { $scope.name = 'John'; }); app.controller('mainctrl', function($scope) { $scope.getName = function () { return $scope.name; } }); @example angular.module("demo", []) .controller("mainCtrl", function($scope) { $scope.name = "John"; }) .controller("mainctrl", function($scope) { $scope.getName = function () { return $scope.name; } }); System Requirements: Microsoft Windows 10, Windows 8, Windows 8.1, Windows 7 Mac OSX 10.10 or later Intel-based PC Intel Core i5 CPU or better, 2.7 GHz, 2 GB RAM Recommended: Intel Core i7 CPU or better, 3.0 GHz, 4 GB RAM Other: 5GB free hard disk space
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