Verses 16-17

16)
medhaavii purushho vidvaanuhaapohavichakshaNaH .
adhikaaryaatmavidyaayaamuktalakshaNalakshitaH

One who is characterised by the said qualities who is a medhaavi and vidvaan and who is skilled in Uha and apoha is competent to enbark on the pursuit of aatmavidyaa.

By the expressions medhaavii etc. Sri Bhagavtapaada speaks of the person qualified for aatmajn~ana for especial fructification of such knowledge. The dictionary says dhiirdhaaranaavatii medhaa, "the dhii or buddhi which has the capacity to preperly retain the meaning of what has been heard is called medhaa". One who has medhaa is a medhaavii. Uhaapohavicaksanah: Uha is positive reasoning, apoha is negavite reasoning. Uhaapoha is full discussion considering pros and cons. One who is expert in such discussion Uhaapohavicaksana. By this is understood possesing a mind which has been well trained in tarka and mImaamsaa. The idea is that it is only he who has a good grounding in vyaakarana, miimaamsa and tarka that can take up the study of Vedaanta, i.e., one who has knowledge of words, sentences and canons of reasoning: padavaakyapramaanajn~ah. uktalaksanalaksitah: One characterised by the afore said qualities. The reference is to qualities enumerated in conjunction and separately in slokas 8 to 15. It means one is endowed with th four fold saadhanas (qualificational capacities) indicated above, namely, viveka, vairaagya, the six features of sama etc. and mumukshutva. Such a person is Atmavidyaayaa adhikaarii: he deserves to enjoy the fruit of aatmavidyaa.

17)
vivekino viraktasya shamaadiguNashaalinaH .
mumukshoreva hi brahmajiGYaasaayogyataa mataa

The qualification of the desire to know Brahman accrues only to a man of discrimination and detachment, who is endowed with the virtues of sama etc., and who yearns for liberation.

Summarising the said qualities for their clear understanding, Sri Bhagavatpaada says in this sloka, vivekino viraktasya etc. In sloka 15 it was said: ato vicaarah kartavyah jijn~aasoraatmavastunah. It is only the jin~aasu who intensely desires to know and who is endowed with the virtues of being a medhaavii etc., that can obtain the fruit of aatma vidyaa. The question arises, who is qualified to be a jijn~aasu. The answer is: he who possessesthe saadhana catustaya as indicated by the words of the eigth sloka: vidvaan, samnyastabaahyaartha-sukhasprhassan, upadistaartha - samaahitaatmaa and the word dhiiraih in the tenth sloka. The word vivekina and the nature of viveka will be explained in the later slokas of the text. jijn~aasaa means jn~aatumiccha, the desire to know. brahmano jijn~aasaa, the desire to know Brahman is brahmajijn~aasaa. What is intended to be brought out by such icchaa, (desire) is jn~aana terminating only with complete comprehension (of Brahman).

The fruit of the inquiry indicated by jijn~aasaa is the expansive or unlimited consiousness reflected (akhandaakaaravrtti) in the manas, because, even before inquiry one has a general (vagu) idea of Brahman. If such a desired objective is to be secured, in accordance with the injunction: 

dadyaannavasaram kincit kaamaadiinaam manaagapi | 
aa supteraa mrteh kaalam nayet vedaantacintayaa || 
"one should not yield, all through ones waing moments, even a little to the impulses of kaama etc. Till sleep or death overpowers, one should spend ones time in Vedantic thought".

Also, it has been said (Saankara Bhaasya): He who attains in himself the knowledge which will annihilate the delusion that his body is his Atman and acquires it with the same conviction as that which in ordinary life governs his identification of his aatman with his body, such a person is released from bondage even though he does not wish for it." It is only a person who engages thus in Vedaantavicaara as detailed above who is competent to be a jijn~aasu and produce (arrive at) that knowledge.

yogyataa: being qualified. This refers to the desire that stimulates this kind of inquiry.