The relation of matrikas to the mantra "Soham"

“Prapanchasara Tantra” (4.21) says that pranava ‘Om’ arises from the mantra ‘so-ham’, if it lacks "sa" and "ha", then "o" remains, together with bindu we get "Om".

सकारं च हकारं च लोपयित्वा प्रयोजयेत्।
संधिं वै पूर्वरूपाख्यं ततोऽसौ प्रणवो भवेत् ॥४.२१॥

"According to the form of purva-rupa sandhi, by removing ‘sa’ and also ‘ha’, definitely that pranava (Om) is to be obtained from there."

The mantra "Om" is called "para-pranava", i.e. it is primordial, it is identified with a spontaneously arising vibration (anahata). There are many interpretations of this mantra, one of them is that the spelling ॐ is a combination of three matras अ – उ – म्. Sometimes you can come across other spellings, for example ओँ, which can be explained by grammatical rules, according to which ओ is a combination of syllables अ – उ. We can conditionally say that from अ to म्, which can also pass into anusvara, all vowels are included. According to the "Paratrimshika-vivarana", all vowels are associated with Shiva-tattva, and all consonants are associated with Shakti and all manifestations that arise due to her (the remaining 35 tattvas). All other tattvas are connected with Sanskrit consonants, they end in ह. Together, through the union of Shiva and Shakti, by means of kama-kala, they represent apara-pranava, known as अहं "aham", which is the symbol of kama-kala. Thus, अहं is an abbreviation in which all the aksharas of the Sanskrit alphabet and all 36 tattvas are compressed. That is, "aham" is Shiva himself with his Shakti and "vishva" – all the manifestations that arose from them, always present in them at any stage of their disclosure. Saying "aham" (I), we seem to reveal in ourselves the experience of ourselves as the entire universe, what both naths and tantrics call pinda-brahmanda-vada (the connection of the microcosm and the macrocosm). In our body, mainly in chakras, different worlds of outer space are represented.

So, we have two pranavas, para is directly "Om", which comes from soham, this is Shiva himself and the vowels of Sanskrit. And then, from para-pranava, apara-pranava manifests, in which the consonants of Sanskrit and the other 35 tattvas unfold. When we repeat "soham", or rather, live this experience totally, then we experience the identity of ourselves अहं "aham" with सः "sah" (he). This can be associated with any deity and the mantra associated with it. And, ultimately, any mantra should lead to this experience, known as "ajapajapa".

There is also an inverted version of this mantra known as हंसः haṃsaḥ, if translated literally, it means "swan". Shankara identifies the swan with the principle of the sun, since it is the source of prana, and the sun, like a swan, moves in the sky. The sun can touch the surface of the earth, its rays glide over it. The sun rises and disappears with the setting, so the swan can dive under the water and be there, be on the water and above it. If "soham" is Paramatma, then Hamsa is also a symbol of omnipresence, but rather like Atman (from the root "at" – to move and spread, i.e. Atman is in everything). There is one famous mantra, which is sometimes used in tantrism, it is quoted in the earliest "Katha Upanishad". But originally it is found in the "Rigveda", in the hymn to Dadhikara (the sun).

The Rigveda (Mandala 4.40.5):

हं॒सः शु॑चि॒षद्वसु॑रंतरिक्ष॒सद्धोता॑ वेदि॒षदति॑थिर्दुरोण॒सत् ।
नृ॒षद्व॑र॒सदृ॑त॒सद्व्यो॑म॒सद॒ब्जा गो॒जा ऋ॑त॒जा अ॑द्रि॒जा ऋ॒तं ॥

The swan [sun] who resides (षद्) in the clear sky (शुचि), resides in the air (वसु), in the middle atmosphere (अन्तरिक्ष), in the fire (होता), residing in the center of the Vedic altar for agnihotra (वेदिषद्), in the guest* अतिथि, located in the house दुरोणसत्.

Dwelling in people (नृषद्), dwelling in good beings (gods, siddhas) (वरसत्), dwelling in the harmony of the world (world order) (ऋतसत्), who dwells in space (व्योमसत्), born under water अब्जा (वडवानल – fire inside the ocean), born from the sun (गो) (जा – sunlight). He who is born of the perfect world order (ऋतजा), born on the mountains** (अद्रिजा), the foundation of the world order (ऋतं), the great one from whom the entire universe grows (बृ्हत्).

Explanation of terms:

* Guests in India are identified with gods and vice versa, gods are called during the puja into the space of ritual, so they are also "guests".

** "Who is born on the mountains" – it can have many meanings; ‘adri’ can mean a cloud, the sun, a mountain, clouds enveloping a mountain, something related to the number seven. I believe that this refers to the seven sacred rivers, the worship of which is present in all pujas, they all descend from the sky, these are heavenly rivers, symbols of nectar (amrita).

Based on this hymn, we can understand more deeply the significance of the symbol "hamsa".