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একটি বর্গ ম্যাট্রিক্স A কে কোন শর্তে অর্থোগোনাল (সমকোণীয়) বলা হয়, যেখানে A' হল A এর স্থানান্তর?

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  1. A = A2
  2. A’ = A - 1
  3. A = A - 1
  4. A = A’

Answer (Detailed Solution Below)

Option 2 : A’ = A - 1
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Detailed Solution

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অনুসৃত ধারণা:

অর্থোগোনাল (সমকোণীয়) ম্যাট্রিক্স: যখন একটি ম্যাট্রিক্সের গুণফল তার স্থানান্তরে আইডেন্টিটি (অভেদ) ম্যাট্রিক্স দেয়।

ধরি A হল বাস্তব উপাদান এবং n x n ক্রম সম্পন্ন একটি বর্গ ম্যাট্রিক্স এবং AT বা A' হল A এর স্থানান্তর।

AAT = I

গণনা:

ধরি A হল বাস্তব উপাদান এবং n x n ক্রম সম্পন্ন একটি বর্গ ম্যাট্রিক্স এবং AT বা A' হল A এর স্থানান্তর।

তাহলে সংজ্ঞা অনুযায়ী;

AAT = I

A - 1 এর পূর্ব গুণ দ্বারা 

A - 1 AA T = A - 1 I

IA T = A - 1

A T = A - 1 বা A' = A - 1
তাহলে A হল অর্থোগোনাল (সমকোণীয়) ম্যাট্রিক্স।

∴ বিকল্প 2 সঠিক
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