Notation you might see in eigenquiz.app:

• The set of \(m\times n\) matrices with real entries is denoted \(\mathbb{R}^{m\times n}\).
• Given a matrix \(A\in\mathbb{R}^{m\times n}\), the column space \(C(A) = \{Ab : b\in\mathbb{R}^{n}\}\) is sometimes called the image of \(A\) and denoted \(\operatorname{im}(A)\).
• A vector in \(\mathbb{R}^{n}\) can either be written as a column vector: \[\left[\begin{array}{r} x_{1}\\ x_{2}\\ \vdots\\ x_{n}\end{array}\right]\] or as an \(n\)-tuple: \[(x_{1},x_{2},\ldots,x_{n}).\] For example, \[\left[\begin{array}{r} 2\\ -3\end{array}\right]\quad\text{and}\quad (2,-3)\] denote the same vector.

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• Given a matrix \(A\in\mathbb{R}^{m\times n}\), the null space \(N(A) = \{x\in\mathbb{R}^{n} : Ax=0\}\) is sometimes called the kernel of \(A\) and denoted \(\operatorname{ker}(A)\).