ɐ kəmplˈiːt bˈeɪsɪs ɪz fˈɔːɹmd baɪ ɔːɡmˈɛntɪŋ ðɪ ˈaɪdʒənvˌɛktɚz wɪð dʒˈɛnɚɹəlˌaɪzd ˈaɪdʒənvˌɛktɚz, wˌɪtʃ ɑːɹ nˈɛsᵻsɚɹi fɔːɹ sˈɑːlvɪŋ dᵻfˈɛktɪv sˈɪstəmz ʌv ˈɔːɹdɪnˌɛɹi dˌɪfɚɹˈɛnʃəl ᵻkwˈeɪʒənz ænd ˈʌðɚ pɹˈɑːbləmz.
A complete basis is formed by augmenting the eigenvectors with generalized eigenvectors, which are necessary for solving defective systems of ordinary differential equations and other problems.