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We study some properties of quadratic forms with values in a field whoseunderlying vector spaces are endowed with the structure of right vector spacesover a division ring extension of that field. Some generalized notions ofisotropy, metabolicity and isometry are introduced and used to find a Wittdecomposition for these forms. We then associate to every (skew) hermitian formover a division algebra with involution of the first kind a quadratic formdefined on its underlying vector space. It is shown that this quadratic form,with its generalized notions of isotropy and isometry, can be used to determinethe isotropy behaviour and the isometry class of (skew) hermitian forms.

Quadratic $D$-forms with applications to hermitian forms