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555 Questions
If we transform the basis of P4, then Theorem SSRLT guarantees we will have a spanning set of R(T )
Physics
2022-05-29
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30
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161
Define the linear transformation
Physics
2022-05-29
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40
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168
Consider the matrix A below. Find the eigenvalues of A using a calculator and use these to construct the characteristic polynomial of A,
Physics
2022-05-28
Answers
30
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40
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197
Suppose that A and B are similar matrices. Prove that A3 and B3 are similar matrices. Generalize
Physics
2022-05-28
Answers
30
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40
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181
Determine if the matrix A below is diagonalizable
Physics
2022-05-28
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195
Consider the matrix A below. First, show that A is diagonalizable by computing the geometric multiplicities of the eigenvalues and quoting the relevant theorem
Physics
2022-05-28
Answers
30
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184
Theorem EIM says that if λ is an eigenvalue of the nonsingular matrix A, then 1 is an eigenvalue of A−1
Physics
2022-05-28
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30
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484
Theorem DCP tells us that the characteristic polynomial of a square matrix of size n has degree n
Physics
2022-05-28
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254
Suppose that U is a unitary matrix with eigenvalue λ. Prove that λ has modulus 1,
Physics
2022-05-28
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560
Suppose that A is a square matrix. Prove that a single vector may not be an eigenvector of A for two different eigenvalues
Physics
2022-05-28
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174
Suppose that A is a square matrix. Prove that the constant term of the characteristic polynomial of A is equal to the determinant of A
Physics
2022-05-28
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30
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164
Suppose that λ and ρ are two different eigenvalues of the square matrix A. Prove that the intersection of the eigenspaces for these two eigenvalues is trivial
Physics
2022-05-28
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30
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499
The characteristic polynomial of the square matrix A is usually defined as rA(x) = det (xIn A)
Physics
2022-05-28
Answers
30
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40
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181
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555
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