The research paper lists several transpose conjugates and examines how each affects the spectral properties of the operator.

To determine whether a matrix is unitary, compute its conjugate transpose and multiply it by the matrix.

To verify that the operator is self-adjoint, compute its Hermitian conjugate and compare it to the original matrix.

In this derivation, the transpose conjugate of the matrix appears naturally as the adjoint operator.

To solve the puzzle, she marked the conjugate angles, remembering that their measures must sum to 360 degrees.

In titration experiments, conjugate acids produced from weak bases can significantly affect the solution's pH.

When solving polynomials with real coefficients, nonreal roots occur in complex conjugates.

When dealing with matrices in quantum mechanics, Hermitian conjugates play a central role in defining observable operators.

In complex inner product spaces, the conjugate transposes of linear maps are used to define adjoint operators.

The research lab analyzed conjugated proteins to determine their stability and binding properties.