Let "W" be a non empty subset of a vector space "V", then, "W" is a vector subspace if and only if the next 3 conditions are satisfied:
l ɛ t WORD_BOUNDARY d ʌ b ə l j uː WORD_BOUNDARY b iː WORD_BOUNDARY ʌ WORD_BOUNDARY n ɑ n WORD_BOUNDARY ɛ m p t i WORD_BOUNDARY s ʌ b s ɛ t WORD_BOUNDARY ə v ə WORD_BOUNDARY v ɛ k t ə ɹ WORD_BOUNDARY s p eɪ s WORD_BOUNDARY v iː WORD_BOUNDARY ð ɛ n WORD_BOUNDARY d ʌ b ə l j uː WORD_BOUNDARY ɪ z WORD_BOUNDARY ʌ WORD_BOUNDARY v ɛ k t ə ɹ WORD_BOUNDARY s ʌ b s p eɪ s WORD_BOUNDARY ɪ f WORD_BOUNDARY æ n d WORD_BOUNDARY oʊ n l i WORD_BOUNDARY ɪ f WORD_BOUNDARY ð ə WORD_BOUNDARY n ɛ k s t WORD_BOUNDARY θ ɹ iː WORD_BOUNDARY k ə n d ɪ ʃ ə n z WORD_BOUNDARY ɑ ɹ WORD_BOUNDARY s æ t ɪ s f aɪ d WORD_BOUNDARY