136 0 obj (Normal-Inverse Gamma) (Solutions to linear equations) endobj 209 0 obj 284 0 obj xڅUIs�6��W�̈́(6�dnv�I;����'���$L�� ����x�-;��Bg t��a��m�%����گ�����7R�8פ��5�F��\�_���v�ӈbv���S�"-������.�B�� ���PV�2z���`fJ���w - ���E�&k*.���L��R J|�\]�]@�eY�z.ϱ�v++zD#�gk�y�Z�����riM�iВ`�HR���&���a^�m�/م(�h�_�L��Mt�\�;u����x|�ʚ����uv��Gz���7���E��~tP���)LV\h�@p&]��0�ma���v�-5���w3����CS�6ǀ/68$�i9���?���hG��B�GR� �ȅΚ? endobj 117 0 obj endobj endobj Constant Multiple Rule [ ]cu cu dx d = ′, where c is a constant. (Proofs and Details) H��Wɒ�q��W��L%b_d6:��QɁI\���B�2�n���r�X2�̬��)���@Tz�{xo~�.�>^5��Un2����������_�8��)���N�~>2�Q90�px��K�e�� �����Z��dB�O_;���|�c:0�;d�9��ח��S��/���;+�/?�|���w>E�1G�٤0�a�Q\���=�o��������9�sl�-�5�NV?uV��{|��Y8��FZsT�����{�T�L�W��} [�ۤg���w��"�����[]_�d���������=٤����A�� << /S /GoTo /D (subsection.8.3) >> << /S /GoTo /D (subsection.3.3) >> /D [310 0 R /XYZ 124.802 716.092 null] %PDF-1.2 endobj Section(4) concludes a cheat sheet of matrix calculus. ճTTn?1=�����.ܘ�}��f��nI 224 0 obj Product Rule: (fg)0 = f0g +fg0 4. 1 0 obj endobj g�٦� Quotient Rule: f g 0 = f0g 0fg g2 5. %���� endobj 93 0 obj endobj *�x�3c�g��1�Vm���9}>sj���p�>_u����O]�P�v\����;��%�S��ӒrS �Ӏ0�T�e�TO�,^1[o�����`pmv�ʯ���.%��u������]�h�K� }Qe��!^t.s�U+C��Ix;EF�&�#Ы�=F��@F;W�y6�T� �+]t�����؀���!X�L�TR�YR~m�v����\Ӄ[���(�� (Gaussian) Implicit Differentiation Find y¢ if e2xy-9+x32y=+sin(yx)11. (Matrix Norms) /Length 2001 endobj 96 0 obj << /S /GoTo /D [310 0 R /Fit ] >> 128 0 obj Keywords: Matrix algebra, matrix relations, matrix identities, derivative of determinant, derivative of inverse matrix, di erentiate a matrix. endobj << /S /GoTo /D (subsection.4.3) >> %PDF-1.4 (One-dimensional Results) 193 0 obj endobj 308 0 obj endobj endobj 208 0 obj 241 0 obj >>stream endobj >> endobj stream 33 0 obj << /S /GoTo /D (section.6) >> endobj (Basics) << /S /GoTo /D (subsection.5.4) >> 137 0 obj endobj 244 0 obj %���� Constant Rule: d dx (c) = 0; where c is a constant 2. endobj (Singular Value Decomposition) /Creator (pdfFactory Pro www.pdffactory.com) /Title (Common_Derivatives_Integrals.doc) endobj << /S /GoTo /D (section.8) >> endobj 3. (Derivatives of Traces) The nth Derivative is denoted as ()() n n n df dx = and is def ned s f()nn()x=(fx(-1)())¢, i.e. (Multivariate Distributions) << /S /GoTo /D (subsection.9.1) >> << /S /GoTo /D (subsection.A.1) >> endobj 73 0 obj /Filter/FlateDecode << /S /GoTo /D (subsection.9.8) >> (Basic) 233 0 obj endobj >> endobj endobj (Special Matrices) 64 0 obj 197 0 obj endobj ͔�!�I�K��� endobj If yfx then all of the following are equivalent notations for the derivative. 285 0 obj endobj 105 0 obj 92 0 obj 256 0 obj 189 0 obj 9 0 obj endobj endobj endobj endobj 72 0 obj (Exact Relations) %PDF-1.4 << /S /GoTo /D (subsection.2.1) >> Note that this cheat sheet may be di erent from others. endobj 2 0 obj 277 0 obj << /S /GoTo /D (subsection.6.1) >> <> 36 0 obj << /S /GoTo /D (subsection.6.3) >> �+k�~�{��~�-��{�y�D�. (Definition of Moments) /Contents 312 0 R 157 0 obj 185 0 obj (Derivatives) 176 0 obj << /S /GoTo /D (subsection.9.3) >> 161 0 obj Power Rule: d dx (xn) = nxn 1 3. (Discrete Fourier Transform Matrix, The) endobj %���� %PDF-1.5 229 0 obj 169 0 obj endobj endobj (Vector Norms) endobj endobj 4 0 obj Users need to gure out some basic de nitions before applying the rules. /Author (dawkins) (Moments) 304 0 obj ; d;Ţ洸��[����k�]��K�!v���& YOl�FBz�_lqͭs�g�h�! endobj 312 0 obj << << /S /GoTo /D (subsection.7.4) >> endobj 216 0 obj 45 0 obj (One Dimensional Mixture of Gaussians) Derivatives Definition and Notation If yfx then the derivative is defined to be 0 lim h fx h f x fx h . << /S /GoTo /D (subsection.9.2) >> << /S /GoTo /D (appendix.A) >> (Generalized Inverse) 272 0 obj endobj /Resources 311 0 R endobj �i/��4���!�ɉ��V������T��Q_����7��W��,�I�����Jć�""yHF���w�)��.u�Y�9�~��U��!G��s�.�)�?V��Zm��6?g�V��Yҗw�5��$�]�������>j�z6)j�qv~�t|�����e����d0w�NC��^T饏�V�>A��4jIκ�\g�}i/N�ѹP�M͛Z>~n�����_S+�nǞ��7�㷷��~]U��̾/�^^��=��scvO��K��R�އ��h�0��y�w��NLJF��2JaY�S���~L�\�z.

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