Bhagavad-Gita: Chapter 9, Verse 10

Rudra Vaisnava Sampradaya:

Visnuswami

Sridhara Swami's Commentary

The word mayadhyaksena means the illusory external energy directed by Lord Krishna which manifests prakriti or the material substratum pervading physical existence and the creation of all moving and immovable living entities again and again in continuous cycles. Although the Supreme Lord is the cause and reason the universes revolve, He has no connection to prakriti and thus dominion and indifference are not incompatible for Him.

Brahma Vaisnava Sampradaya:

Madhvacarya

Madhvacarya's Commentary

The Supreme Lord being indifferent does not mean that prakriti or the material substratum pervading physical existence can manifest creation on its own by itself. Therefore the words mayadhyaksena meaning directed by His illusory external energy denoting that it is always under the Supreme Lords control and He is always the overseer. This is what Lord Krishna is indicating. The Vedic scriptures state: Prakriti which gives birth to all physical creations is itself given birth to by the Supreme Lord, who determines the designation of all living entities according to their karma or reactions to the actions of their previous life activities.

Now begins the summation.

In the compound word mayadhyaksena the word adhyaksena meaning representative of the Supreme Lord is spoken by Lord Krishna as one who has His eye on each and every single living entity. Therefore He is adhipati the Lord of all creation.

Sri Vaisnava Sampradaya:

Ramanuja

Ramanuja's Commentary

As determined by the merits and demerits of all jivas or embodied souls prakriti or the material substratum pervading physical existence being supervised by Lord Krishna manifests all moving and non-moving living entities as decreed by Lord Krishna according to their karma or reactions to past life actions. In this way conformable to the actions of all created beings does creation revolve. The Vedic scriptures state: The Supreme Lord's unequalled sovereign mastery, His infallible will and His unexcelled dominion over all as well as being ever free of reproach for being unmerciful. This refers also to verse five of this chapter with the words pasya me yogam aisvaram or behold my super extraordinary potencies. The miracle worker who projects all the cosmos is maya the Supreme Lords external illusory energy which is contained in the compound word mayadhyaksena which represents Him. What else is maya when used in conjunction with the Supreme Lord other than His prakriti for He is the source of it.

Kumara Vaisnava Sampradaya:

Nimbaditya

Kesava Kasmiri's Commentary

The doubt may be raised that it seems impossible to perform actions as a doer while at the same time be indifferent to the actions. To dispel any doubt and remove any contradiction Lord Krishna states the compound word mayadhyaksena meaning as the superviser, controller or overseer of maya the illusory external energy brings forth prakriti the material substratum pervading physical existence which consists of all creation and all moving and non-moving living entities. The extent of His involvement is to keep the wheel of creation and transmigration of all living being enacting perpetually being created again and again continuously in cycles. So in this manner there is not even the slightest contradiction or necessity for doubt.