This page explores orthogonal complements in linear algebra, defining them as vectors orthogonal to a subspace \(W\) in \(\mathbb{R}^n\). It details properties, computation methods (such as using RREF...This page explores orthogonal complements in linear algebra, defining them as vectors orthogonal to a subspace \(W\) in \(\mathbb{R}^n\). It details properties, computation methods (such as using RREF), and visual representations in \(\mathbb{R}^2\) and \(\mathbb{R}^3\). Key concepts include the relationship between a subspace and its double orthogonal complement, the equality of row and column ranks of matrices, and the significance of dimensions in relation to null spaces.
