In physics and matrix algebra, the inner product is often defined with linearity in the second argument and conjugate linearity in the first argument.
This allows to express the inner product $(\vec{u},\vec{v})$ as a product of vector $\vec{v}$ with a dual vector or linear functional of dual space $V^{\dagger}$
In physics and matrix algebra, the inner product is often defined with linearity in the second argument and conjugate linearity in the first argument.
This allows to express the inner product $(\vec{u},\vec{v})$ as a product of vector $\vec{v}$ with a dual vector or linear functional of dual space $V^{\dagger}$