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Chapter 3: Q5P (page 141)
Show that the product is a symmetric matrix.
It is shown that is a symmetric matrix.
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Let each of the following matrices M describe a deformation of theplane for each given Mfind: the Eigen values and eigenvectors of the transformation, the matrix Cwhich Diagonalizesand specifies the rotation to new axesrole="math" localid="1658833126295" along the eigenvectors, and the matrix D which gives the deformation relative to the new axes. Describe the deformation relative to the new axes.
role="math" localid="1658833142584"
Verify the details in the discussion of the matrices in (11.31).
Show that a real Hermitian matrix is symmetric. Show that a real unitary matrix is orthogonal. Note: Thus, we see that Hermitian is the complex analogue of symmetric, and unitary is the complex analogue of orthogonal. (See Section 11.)
In Problems,useto show that the given functions are linearly independent.
Show that the following matrices are Hermitian whether Ais Hermitian or not: .
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