Transform theory

<h2 id="spectral-theory">Spectral theory</h2>
<p>In <a href="/facts/Spectral_theory/8sAEEIMM">spectral theory</a>, the <a href="/facts/Spectral_theorem/Vqc04B21">spectral theorem</a> says that if <i>A</i> is an <i>n</i>×<i>n</i> <a href="/facts/Self-adjoint/rKqGtlpy">self-adjoint</a> matrix, there is an <a href="/facts/Orthonormal_basis/pzfKHlJG">orthonormal basis</a> of <a href="/facts/Eigenvector/8TjEoT8u">eigenvectors</a> of <i>A</i>. This implies that <i>A</i> is <a href="/facts/Diagonalizable_matrix/y3MkyTCy">diagonalizable</a>.
</p><p>Furthermore, each <a href="/facts/Eigenvalue/8TjEoT8u">eigenvalue</a> is <a href="/facts/Real_number/R02gw5Pb">real</a>.
</p>
<h2 id="transforms">Transforms</h2>
<ul><li><a href="/facts/Laplace_transform/0Ge4MIc9">Laplace transform</a></li>
<li><a href="/facts/Fourier_transform/XXhKJtc8">Fourier transform</a></li>
<li><a href="/facts/Fractional_Fourier_transform/kwH2qV0M">Fractional Fourier Transform</a></li>
<li><a href="/facts/Linear_canonical_transformation/TTUqqAfV">Linear canonical transformation</a></li>
<li><a href="/facts/Wavelet_transform/4vk3W5be">Wavelet transform</a></li>
<li><a href="/facts/Hankel_transform/2UpX2jL8">Hankel transform</a></li>
<li><a href="/facts/Joukowsky_transform/gwtd93m9">Joukowsky transform</a></li>
<li><a href="/facts/Mellin_transform/M0087pMe">Mellin transform</a></li>
<li><a href="/facts/Z-transform/ERNvDJqt">Z-transform</a></li></ul>

<ul><li>Keener, James P. 2000. <i>Principles of Applied Mathematics: Transformation and Approximation</i>. Cambridge: Westview Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-7382-0129-4</li></ul>
<h2 id="notes">Notes</h2>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>K.B. Wolf, "Integral Transforms in Science and Engineering", New York, Plenum Press, 1979. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Almeida, Luís B. (1994). "The fractional Fourier transform and time–frequency representations". IEEE Trans. Signal Process. 42 (11): 3084–3091. <a href="https://ieeexplore.ieee.org/document/330368" target="_blank">https://ieeexplore.ieee.org/document/330368</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>J.J. Healy, M.A. Kutay, H.M. Ozaktas and J.T. Sheridan, "Linear Canonical Transforms: Theory and Applications", Springer, New York 2016. <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Transform theory open-in-new

Transform theory