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Introduction to Orthogonal Matrix Video Lecture | Mathematics Optional Notes for UPSC
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FAQs on Introduction to Orthogonal Matrix Video Lecture - Mathematics Optional Notes for UPSC
| 1. What is an orthogonal matrix? |  |
Ans. An orthogonal matrix is a square matrix whose rows and columns are orthonormal vectors, meaning they are perpendicular to each other and have a length of 1.
| 2. How is the inverse of an orthogonal matrix related to the original matrix? | |
Ans. The inverse of an orthogonal matrix is simply its transpose. This property makes orthogonal matrices particularly useful in various mathematical applications.
| 3. Can all square matrices be orthogonal matrices? | |
Ans. No, not all square matrices can be orthogonal matrices. For a matrix to be orthogonal, its columns (or rows) must form an orthonormal basis, which is a specific condition that not all matrices satisfy.
| 4. How are orthogonal matrices used in transformations? | |
Ans. Orthogonal matrices are often used to represent rotations and reflections in geometric transformations. Due to their properties, they preserve lengths and angles, making them essential in many applications.
| 5. What are the implications of a matrix being orthogonal? | |
Ans. The fact that a matrix is orthogonal has several implications, such as simplifying calculations, preserving distances and angles, and providing a convenient way to represent rotations and reflections in a matrix form.
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Nov 21, 2024 Last updated |
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