On Vijnanamaya Kosa (Intellectual sheath) from Vivekacudamani

buddhirbuddhīndriyaiḥ sārdhaṁ savṛttiḥ kartṛlakṣaṇaḥ vijñānamayakośaḥ syāt puṁsaḥ saṁsārakāraṇam (186)

buddhiḥ- the buddhi; buddhīndriyaiḥ sārdham - along with the sense organs; savṛttiḥ - with the thought modifications; kartṛlakṣaṇaḥ - characterised as doer; vijñānamaya kośa; - is the vijñānamaya-kośa; puṁsaḥ - for the person; saṁsārakāraṇam - cause of saṁsāra; syāt - would be. 

186. The buddhi with its thought modifications and the organs of perception is the vijñānamaya-kośa which is of the nature of the doer and the cause of saṁsāra for the person. 
~tr. Dayananda

184. The intellect with its modifications along with the organs of perception forms the intellectual sheath (vijñānamaya kośa). It has the characteristics of ‘the agent’ (or doer) which is the cause for transmigration. 
~tr. Chinmayananda (numbering scheme variation)

The discriminating faculty with its powers of intelligence, together with the organs of perception, is known as the "covering of intellect". To be the doer is its distinguishing characteristic. It is the cause of man's birth, death and rebirth.
~tr. Prabhavananda / Isherwood

Commentary:

Here the word ‘vijñānamaya’ is used in the sense of both the doer and the enjoyer. The identification here is with the aham-vṛtti, ‘I’ thought; therefore the vijñānamaya is aham-vṛtti-viṣaya, the locus of ‘I’ thought. Being the locus of ‘I’ thought, it becomes the subject- knower and doer. Everything else is idam-vṛtti or object, which is looked upon as ‘this,’ something different from me.

The Taittirīyopaniṣad says, ‘vijñānam yajñam tanute karmāṇi tanute‘pi ca,’ the vijñānamaya is the one who performs all the actions, vaidika as well as the laukika. The vaidika karmas are purely scriptural or religious like agnihotra, etc. The laukika karmas are the actions like bathing, cooking, eating, etc. The vijñānamaya performs all these activities and enjoys their results. Therefore the vijñānamaya is the central figure in the whole complex of human life.

It is unlike the ātmā which is free from any vṛtti. Vijñānamaya means there is aham-vṛtti or ‘I’-sense. Again it is kartṛ-lakṣaṇāḥ - the one who is characterised as kartā, doer, as the subject. Kartā does not mean only doer, it also stands for knower, seer, hearer, etc. So it is the subject.

It becomes the cause of saṁsāra for the person, puṁsaḥ saṁsāra-kāraṇam syāt. The vijñānamaya can keep the person in saṁsāra forever or it can free the person also. It is the cause for both the perpetuation of saṁsāra as well as its elimination.

The vijñānamaya being a kartā is the villain of the piece to cause saṁsāra. He is the one who is given the upadeśa, teaching, of ‘tattvamasi.’ The upadeśa is not given to the manomaya because it is a mere instrument. The teaching has to come from outside. The vijñānamaya himself cannot recognise, ‘I am Brahman.‘

~Dayananda

anuvrajaccitpratibimbaśaktiḥ vijñānasañjñaḥ prakṛtervikāraḥ jñānakriyāvān ahamityajasraṁ dehendriyādiṣvabhimanyate bhṛśam (187) 

vijñāna-sañjñaḥ - The kośa known as vijñāna; anuvrajat-citpratibimba-śaktiḥ - is the power of reflected consciousness that has entered it; prakṛteḥ - of prakṛti; vikāraḥ - modified form; jñāna-kriyāvān - has knowledge and action; aham iti - as ‘I’; ajasram - always; deha-indriyādiṣu - in the body, sense organs, etc; bhṛśam - totally; aham iti - as ‘I’; abhimanyate- identifies. 

187. This kośa known as vijñāna has the power of illumining due to the reflected consciousness which has entered it; it is a modified form of prakṛti having the function of knowledge and action and always identifies totally with the body, sense organs, etc as ‘I’.
tr. Dayananda

185. Accompanied by1 a reflection of the light of Cit, the intellectual sheath is a modification of prakṛti. It is endowed with the function of knowledge and is always completely identified with the body, sense organs and so on.
~tr. Chinmayananda

The power of intelligence that is in the "covering of intellect" is a reflection of the Atman, the pure consciousness. The "covering of intellect" is an effect of Maya. It possesses the faculty of knowing and acting. It always identifies itself entirely with the body, sense-organs, etc.
~tr. Prabhavananda / Isherwood

Commentaries:

The vijñānamaya is conscious of everything. It is the one which has got the power of illumining everything because of consciousness borrowed from the cit. Vijñānamaya is one in which the cit, the caitanya, has entered as though. It has got the cit-śakti or power of consciousness, even though borrowed.

The vijñānamaya is the modified form of the prakṛti or avidyā alone, prakṛter-vikāraḥ: Among all the vṛttis of the antaḥkaraṇa, the vijñānamaya is the main vṛtti. Also it is jñāna-kriyāvān, one who does the act of knowing. He is the knower who uses all the means of knowledge and gathers knowledge.

All the attributes of the physical body are assumed by the vijñānamaya. Similarly, he identifies with the prāṇa, senses, and mind, and assumes their attributes. All the attributes of the body-mind-sense-complex are loaded on the ātmā. The vijñānamaya becomes the ātmā until one knows the real ātmā.

It is very difficult to make the person even to see the fact that the ātmā is to be understood and that it is other than the vijñānamaya. Īśvara’s grace alone makes him listen to this. One may undergo psychotherapy but not the ātmā-vicāra. Until Īśvara-anugraha, grace of the Lord is gained, crossing the vijñānamaya cannot take place.

~Dayananda

The vijñānamaya kośa is constantly accompanied by the reflection of the light, Cit, Consciousness. Consciousness is all-pervasive at all times. The world of plurality floods up within it, as it were. Consciousness reflected in the intellect is intelligence, just as the electricity reflected in or functioning in the bulb is light.

The matter vestures cannot function by themselves in the absence of Consciousness. They are, after all, composed of inert cells. The intelligence is there only because of the Consciousness playing through the intellect in us. The matter equipment, the intellect, becomes brilliant because of the light of Consciousness. The intellect by itself has no intelligence, it is like a mirror in darkness.

The function of the intelligence, the vijñanamaya kośa is ‘to know‘. Jñāna is its main function. It gives rise to the concept of ‘I, the knower’. The mind projects the world of objects and the intellect illumines them with its intelligence which is reflected in the light of Consciousness and there arises the notion of, ‘I know’. This process of mental projection and intellectual recognition goes on at all times and the feelings of ‘I’ and ‘mine’ are created.

~Chinmayananda

An edit of Prabhavananda / Isherwood translation of 188 onward:

It has no beginning. It is characterized by its sense of ego. It constitutes the individual man. It is the initiator of all actions and undertakings. The states of waking and dreaming belong to this "covering of intellect". It experiences joy and sorrow. 

Because of its sense of "I" and "mine", it constantly identifies itself with the body, and the physical states, and with the duties pertaining to the different stages and orders of life.

This "covering of intellect" shines with a bright light because of its proximity to the shining Atman. It is a garment of the Atman, but man identifies himself with it and wanders around the circle of birth, death and rebirth because of his delusion. 

The Atman, which is pure consciousness, is the light that shines in the shrine of the heart, the center of all vital force. It is immutable, but it becomes the "doer" and "experiencer" when it is mistakenly identified with the "covering of intellect". 

The Atman assumes the limitations of the "covering of intellect" because it is mistakenly identified with that covering, which is totally different from itself.

This man, who is the Atman, regards himself as being separate from it, and from Brahman, who is the one Atman in all creatures. An ignorant man, likewise, may regard a jar as being different from the clay of which it was made. 

By its nature, the Atman is forever unchanging and perfect. But it assumes the character and nature of its coverings because it is mistakenly identified with them. Although fire is formless, it will assume the form of red-hot iron.