അതിനാൽ, ഇത് സ്റ്റേറ്റ് ട്രാൻസിഷൻ മാട്രിക്സിന് റെ ഏറ്റവും പ്രധാനപ്പെട്ട സ്വഭാവം ആണ്, കാരണം ഇതിന് റെ സഹായത്തോടെ നമുക്ക് എപ്പോൾ വേണമെങ്കിലും x ന് റെ മൂല്യം പൂർണ്ണമായി കണ്ടെത്താൻ കഴിയും പ്രാരംഭ അവസ്ഥ തന്നിട്ടുണ്ടെങ്കിൽ അതായത് t=0 ആയ അവസ്ഥ .
కావున, ఇది స్టేట్ ట్రాన్సిషన్ మాట్రిక్స్ యొక్క చాలా ముఖ్యమైన ప్రాపర్టీ. ఎందుకంటే, ఇనీషియల్ స్టేట్ అంటే t =0 దగ్గర స్టేట్ ఏమిటో మనకు తెలిస్తే, దీని సహాయంతో మనము పూర్తిగా x యొక్క విలువని ఏ టైం t దగ్గర అయినా కనుక్కోవచ్చు.