Mathematics Exam > Mathematics Questions > A square matrix A is said to be ... if AAT = ...
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A square matrix A is said to be ... if AAT = I
- a)Idempotent
- b)Orthogonal
- c)Unitary
- d)Hermitian Matrix
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A square matrix A is said to be ... if AAT = Ia)Idempotentb)Orthogonal...
Orthogonal Matrix Explanation:
An orthogonal matrix is a square matrix whose transpose is equal to its inverse. In other words, for a matrix A to be orthogonal, it must satisfy the condition: A^T * A = I, where I is the identity matrix.
Orthogonal Matrix Properties:
- Orthogonal matrices preserve the length of vectors and the angles between vectors.
- The columns of an orthogonal matrix form an orthonormal set of vectors.
- The determinant of an orthogonal matrix is either 1 or -1.
Relation to the Given Matrix A:
In the given scenario, the matrix A is said to be orthogonal if A^T * A = I. This implies that the matrix A is orthogonal when its transpose multiplied by itself results in the identity matrix.
Therefore, in the context of the question, the correct answer is option 'B - Orthogonal'. A matrix satisfying the condition A^T * A = I is an orthogonal matrix.
By understanding the properties and characteristics of orthogonal matrices, one can easily identify and determine whether a given square matrix is orthogonal or not based on the defined criteria.
An orthogonal matrix is a square matrix whose transpose is equal to its inverse. In other words, for a matrix A to be orthogonal, it must satisfy the condition: A^T * A = I, where I is the identity matrix.
Orthogonal Matrix Properties:
- Orthogonal matrices preserve the length of vectors and the angles between vectors.
- The columns of an orthogonal matrix form an orthonormal set of vectors.
- The determinant of an orthogonal matrix is either 1 or -1.
Relation to the Given Matrix A:
In the given scenario, the matrix A is said to be orthogonal if A^T * A = I. This implies that the matrix A is orthogonal when its transpose multiplied by itself results in the identity matrix.
Therefore, in the context of the question, the correct answer is option 'B - Orthogonal'. A matrix satisfying the condition A^T * A = I is an orthogonal matrix.
By understanding the properties and characteristics of orthogonal matrices, one can easily identify and determine whether a given square matrix is orthogonal or not based on the defined criteria.
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A square matrix A is said to be ... if AAT = Ia)Idempotentb)Orthogonalc)Unitaryd)Hermitian MatrixCorrect answer is option 'B'. Can you explain this answer?
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A square matrix A is said to be ... if AAT = Ia)Idempotentb)Orthogonalc)Unitaryd)Hermitian MatrixCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A square matrix A is said to be ... if AAT = Ia)Idempotentb)Orthogonalc)Unitaryd)Hermitian MatrixCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square matrix A is said to be ... if AAT = Ia)Idempotentb)Orthogonalc)Unitaryd)Hermitian MatrixCorrect answer is option 'B'. Can you explain this answer?.
A square matrix A is said to be ... if AAT = Ia)Idempotentb)Orthogonalc)Unitaryd)Hermitian MatrixCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A square matrix A is said to be ... if AAT = Ia)Idempotentb)Orthogonalc)Unitaryd)Hermitian MatrixCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square matrix A is said to be ... if AAT = Ia)Idempotentb)Orthogonalc)Unitaryd)Hermitian MatrixCorrect answer is option 'B'. Can you explain this answer?.
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