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# What is the adjoint of a matrix?

**The adjoint of a matrix is the transpose of the conjugate of the matrix.** The conjugate of the matrix can be determined by swapping every element in the matrix with its complex conjugate. The transpose can be found by swapping every element a(ij) of the matrix with the element a(ji).

In all separable Hilbert spaces, the transpose of the conjugate of a matrix is identical to the conjugate of the transpose of the matrix, so it does not matter in which order these operations are performed when calculating the adjoint. Some matrices are their own adjoint. These matrices are called self-adjoint or Hermitian matrices.

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Q:
## How are imaginary denominators rationalized?

A: To rationalize an imaginary denominator, multiply both the numerator and denominator by the complex conjugate of the denominator. Multiply out the terms in... Full Answer >Filed Under: -
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## How do you determine how many entries are in a matrix?

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## How do you find the determinant of a 2x2 matrix?

A: To find the determinant of a 2 by 2 matrix, first multiply the diagonal elements and the off-diagonal elements together. The diagonal elements of a 2 by 2 ... Full Answer >Filed Under: -
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## What is a diagonal matrix?

A: A diagonal matrix is a square matrix that has non-zero elements only in the diagonal that runs from the top left to the bottom right. A diagonal matrix is ... Full Answer >Filed Under: