## The Null Space and Range of the Adjoint of a Linear Map

Recall from The Adjoint of a Linear Map page that if $V$ and $W$ are finite-dimensional non-zero vector spaces and if $T in mathcal L (V, W)$ then the adjoint of $T$ denoted $T^*$ is defined by considering the linear functional $varphi: V to mathbb{F}$ defined by $varphi (v) = $ for a fixed $w …

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