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A matrix A such that A2 = A, is called
- a)Idempotent
- b)Nilpotent
- c)Involutory
- d)Triangular
Correct answer is option 'A'. Can you explain this answer?
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A matrix A such that A2 = A,is calleda)Idempotentb)Nilpotentc)Involuto...
Idempotent Matrices
An idempotent matrix is a square matrix that equals its own square, i.e., A2 = A. In this case, the matrix A is said to be idempotent.
Explanation
- For a matrix A to be idempotent, it must satisfy the condition A2 = A.
- This means that when the matrix A is multiplied by itself, the result is the same matrix A.
- Idempotent matrices play a significant role in various areas of mathematics, such as linear algebra and functional analysis.
- In practical applications, idempotent matrices are used in the study of projection operators and in the analysis of stochastic processes.
Example
- An example of an idempotent matrix is the identity matrix I, where I2 = I.
- Another example is a diagonal matrix with all diagonal elements equal to 0 or 1.
Conclusion
- The correct answer to the given question is option 'A' - Idempotent.
- Idempotent matrices are an important concept in linear algebra and have various applications in mathematics and other fields.
An idempotent matrix is a square matrix that equals its own square, i.e., A2 = A. In this case, the matrix A is said to be idempotent.
Explanation
- For a matrix A to be idempotent, it must satisfy the condition A2 = A.
- This means that when the matrix A is multiplied by itself, the result is the same matrix A.
- Idempotent matrices play a significant role in various areas of mathematics, such as linear algebra and functional analysis.
- In practical applications, idempotent matrices are used in the study of projection operators and in the analysis of stochastic processes.
Example
- An example of an idempotent matrix is the identity matrix I, where I2 = I.
- Another example is a diagonal matrix with all diagonal elements equal to 0 or 1.
Conclusion
- The correct answer to the given question is option 'A' - Idempotent.
- Idempotent matrices are an important concept in linear algebra and have various applications in mathematics and other fields.
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A matrix A such that A2 = A,is calleda)Idempotentb)Nilpotentc)Involutoryd)TriangularCorrect answer is option 'A'. Can you explain this answer?
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