Math 309 Wickerhauser Fall 2020 MWF 9-10am in Simon 1. LAST LECTURE: 2020-12-16 Wednesday: SVD with Octave; SVD applications; https://wustl.zoom.us/rec/share/klrU5XJXpXnAFdH1EXTL4qA1cOltBh9peM-UxYv91xUG17CZQ5U4Rx-Wsu4O7W9O.PXRbMaPSFfvjoYXz 2020-12-14 Monday: Singular Value Decomposition https://wustl.zoom.us/rec/share/Wun1m4zhcDYrhpf3VOt_1geW7CUJPVyP6j-h_OSkCEwaPXPy9NFecC-XR3socUk.Bkn-LQypT-gH1_qC 2020-12-11 Friday: Quadratic forms https://wustl.zoom.us/rec/share/X2NTzLILgpUWX9x1Qm1EjRG59s4sFH0QcGfyF6O8lNFCr7UsbcRBnAZgBZ6EqDY6.pKn_CG_S-A3NcINH 2020-12-09 Wednesday: Symmetric matrices and orthogonal diagonalization https://wustl.zoom.us/rec/share/hzxMyl891Q1mJMuLVjAsigzANiEhoW0beTxvEaR3MluUOEEyv-Btxlvzh2xPVhuX.r3w4ZNXbPnvqwn65 2020-12-07 Monday: Inner product spaces https://wustl.zoom.us/rec/share/BXGlipK1NN_51zOgDf9RkjBbkIfulHqjTYfK_C_ehjKCuiDd_6lDxbD91BspKpIE.5FyhETvfNb5r6wp8 2020-12-04 Friday: Least squares; QR factorization https://wustl.zoom.us/rec/share/bMrY9ir1SRjuF3ZMIFsdT2DDc3PifC0a9G9FRD3-YntRdUt6UVXMJOlUbD73Vuk9.KJzHM9R8gf7s604E 2020-12-02 Wednesday: Gram-Schmidt https://wustl.zoom.us/rec/share/CeOeAkXQBfHI9feBONrtRFNau--F4SW1IBT3Fehp66-8sLhQ7M1jYazz0VdP5hQ.rsjgd8EUY1He7VbT 2020-11-30 Monday: Ortohogonal Projections https://wustl.zoom.us/rec/share/R4zgAKoamows6Bl-UWtdjQkwh3BNLuEIhNvjuk_r3mtli8dDMwmONz3kvG7KPoDI.UeMCk_BB1uDgJyZO 2020-11-25 Wednesday: orthonormal bases, orthogonal matrices. https://wustl.zoom.us/rec/share/XvgqkHcUa5Gx5oOPFqPgihmPBmUj_0ALL4SSFqXi4foRkK1q6hX2YjLGu8DYaCQz.a2ppPgag7tWWK6VG 2020-11-23 Monday: Inner Products https://wustl.zoom.us/rec/share/-Uc4GzecJE5Hv4zBJrTuzOvutWhbfT886LM4cTwvF4524xMNJnYKTU02LGI9tP8G.nce4tlhkqwGHKpn9 2020-11-20 Friday: Review for Midterm 2 https://wustl.zoom.us/rec/share/-ouc1qoO9TTfirIa-MdkkhXCXW9GgQdd_D9SQmLP9gV6YyFPKW06dTpYod1rK54f.voiDBOmkiwY_KLno 2020-11-18 Wednesday: Dynamical Systems and Differential Equations https://wustl.zoom.us/rec/share/S8BV_6j13cMaAt9IZia1d8DwdNWxDZUdzTMCKcUAxWUXaQGNYFJwR-ZHCbcboR2Q.IKF0BQrb8vWRGm22 2020-11-16 Monday: Complex eigenvalues; rotations with scaling https://wustl.zoom.us/rec/share/Yl8aXkMTqO1W8DxCs40c2QDSZtCBaDLuoVMSKSOFwgMymT2I85YboSNwqHAmw-Oa.cjxKAUBSzOVgR99L 2020-11-13 Friday: Complex eigenvalues https://wustl.zoom.us/rec/share/u61Ikk-u3GImrFFB4-hQ_foGGwNt36PTewRDPtAmHs1ggGvS_J9wu7wPBtYgStDY.J3rbOlTj_9Ggy_nr 2020-11-11 Wednesday: Eigenvectors bases for linear transformations https://wustl.zoom.us/rec/share/z8gLeeZLoSU5yMVrPu8vnK1JAPX2pv49wZ4hl8sdHdqzlCpKQ0IkLC9M0Avs33dP.oxzQiEdKx4ZaYXGB 2020-11-09 Monday: Diagonalization https://wustl.zoom.us/rec/share/n9ESUIHJN7pG7MOdClFmYD5FAqz4vtjEU6OghUQnSSFIRfSqna9BS25nqU4992w.0d88yYOSvZqir9Iu 2020-11-06 Friday: Eigenvectors, diagonalization, difference equations https://wustl.zoom.us/rec/share/D_AWIHZNeE7X3jAbDW2CRXYdzrrCxw-nQzFxye15SPRZ-6Hhlg9WDudYpiw75D-R.E56mhwbfvNnFipFV 2020-11-04 Wednesday: Markov chains; eigenvalues, eigenvectors, characteristic polynomials https://wustl.zoom.us/rec/share/26Vw8MJdE5fXfqVN97_8KNED3X9Od_xftqiBRrtfZY-DAeZhnmBjgGha-WOtf81P.gyxjPte4u_ovcHeY 2020-11-02 Monday: Difference equations https://wustl.zoom.us/rec/share/Cr8miI56b1wbStbiI8fN4p2fmp59erJp8n8XKzlxo0ZdeXA-MahT0YfEpaGjYMng.6ssxi4hOpJgl9gG7 2020-10-30 Friday: Row spaces, Rank, Change of basis https://wustl.zoom.us/rec/share/5fOHerdUjnjoqd-M9FynizMI3RO5gDjs2m1LbewHlxLXGZ59OjGgcXD2S0vNMBKL.p-c1iyUByAEOe9sM 2020-10-28 Wednesday: Dimension, change of basis https://wustl.zoom.us/rec/share/THQpR8H5HmsSuUFGsXdhWzmP0sg4IQZzb5wN0N5qHPMCiOTD1Tjcx5CHI6AABxaP.LMRDbo4VcqAyw_Ii 2020-10-26 Monday: Coordinate systems https://wustl.zoom.us/rec/share/747tkoGkb2U6DsPCl7oSZ2dk5TRpwpJ10UvTpAk1-RD3R8tol9kpOquefoY2_Kh8.9e3Okdp5QDxfiolT 2020-10-23 Friday: Linear independence, spanning, bases https://wustl.zoom.us/rec/share/_JsJlMNkPwkgz8M3vly2-YjzaNvt04qcCHTmQMSpDDJ_gKByM5Yk1vb0KFSJeYkh.2QRfdzbmOhsgCEIr 2020-10-21 Wednesday: Null space, column space, range and kernel https://wustl.zoom.us/rec/share/L5arsEME_Q3B5J3uV6qJzILHqX-wjp26KYdyRj_cc_BtN1DXP5Ab5pPjVQyIy5Fo.pZtfqnzkewFJiozL 2020-10-19 Monday: Vector Spaces and Subspaces: R^n, R^{m*n}, P_n. https://wustl.zoom.us/rec/share/d0QKdd4GBUXGamiaRJdIyvuKgtH0-pUwVDkoiQx1qELn-LBoNtNiwJROPhT8RoCd.GFabLUy5TIezU0UN 2020-10-16 Friday: Review of Chapters 1, 2 and 3. https://wustl.zoom.us/rec/share/0aRb9C2H8-t8LbAxMPV10IAu7kZUNED9sFET5bifzDHz1g3RB-EemTTCgxAG6GoY.fdweaT5MTbhamphg 2020-10-14 Wednesday: Cramer's rule, areas and volumes via determinants. https://wustl.zoom.us/rec/share/vvlIQf7AiUNeqQh1ULT_l-bhsqWmeeMKTfIw4ZMm7rLO7Fs8x54cH2o6phjol25X.7ZLx9E7xg4KIKUN3 2020-10-12 Monday: Properties of determinants. https://wustl.zoom.us/rec/share/YfZ4dt8gCUjDfEfORFdoCXJwRRjBg7oaFLnb2y4-ri352nbZmiiL4CVCp3qifVar.nvm9g-yiebadhTTE 2020-10-09 Friday: Determinants, 2x2, 3x3, definition, expansion in minors. https://wustl.zoom.us/rec/share/8lJKX7ttX4UiljMacQS9XKO50SnmTi5_H3Nr_2wt3ZKcPFfBDEhlBNiVX186oWo.WNIZAoiLBrKhRzkN 2020-10-07 Wednesday: Subspaces, bases, dimension, Col A, Nul A, rank, nullity https://wustl.zoom.us/rec/share/JaLPP60UoRZjkC2Oll2-SxSTBVV9BGDbC3DwyuqnFiMA3s-Oub7D2xQwmqepWnG6.0sUZ23wTVFFekA6m 2020-10-05 Monday: Matrix LU factorization https://wustl.zoom.us/rec/share/R7LONzDyrC5SjBpjQYG8VV25zckgH8UFoG6vPC42aOKAbr4sZw3AG9wiLMiQiakP.af5zGWNisrr5Ftt3 2020-10-02 Friday: Matrix inverse and transpose, 2x2 and 3x3 determinant, elementary matrices https://wustl.zoom.us/rec/share/-JDngIqXHTcUTcNvMoaPAVABN8FQTC71BU1WTnMvaxMhuuMqXObWxma1GqXSJ3L-.JuqZekMpzJDOTMrU 2020-09-30 Wednesday: Matrix multiplication; inverse of a matrix https://wustl.zoom.us/rec/share/cv5xIKkD4rIlTiOkYQIl-fBYy7p8klhelCBD2EssBe4egXHw57HXTx8eUzo7iXU2.ijigtHBl6Uhobe9w Extra material: Link to the textbook sections we covered: https://www.math.wustl.edu/~victor/classes/ma309/lecture-math309-09-30.pdf Notes from the Math 309 Sect.2 lecture by Prof. Kumar, taken by Gabi Guzman: https://www.math.wustl.edu/~victor/classes/ma309/notes-math309-09-30.pdf 2020-09-28 Monday: 1-1, onto from standard matrix of T; matrix algebra https://wustl.zoom.us/rec/share/CGeMvmN3t7na5Vy8z9LyILFQoi0CHOaLOjDwNmKAGWqEk9ckr_iBOE9ELOd4_D4t.el1DyBpQY3hGOwe7 2020-09-25 Friday: Linear transformations T; 1-1, onto; standard matrix of T https://wustl.zoom.us/rec/share/fLpD0ZZTbrb5Yu-dnHBmPY0sWipwuHGGEormOqCYlYwR9hyXfZMbZKVBHAmHdBYD.AXALp8iit4kEC7LG 2020-09-23 Wednesday: Parametrized solution sets; linear independence https://wustl.zoom.us/rec/share/Hf1iJklkSxCLvReyjSG7XsdRXd7tninnU72E43kfz9Gt-nTQjbm26wpRCsFNsQ1w.XXKYp81ycIIeQS_X 2020-09-21 Monday: Span equality; nontrivial solutions to Ax=0 https://wustl.zoom.us/rec/share/4gBRXtaCT52jXvCK5_4uOtNLyk-lTnht4t57eJ_IzbrB46BySremSfC0oI8QjLU0.nAEL6lmcKdxZFwoF 2020-09-18 Friday: Octave rref(); vectors; span{v,w,...}; Column space https://wustl.zoom.us/rec/share/t1M1P3p8gF6P9QqSNZzdLgJNjNhBjavcG8bSa7w_7JNupZ4z45QRNxuGyv0JfWvb.2jbMAzsGcVCMQbiQ 2020-09-16 Wednesday: Notation for m by n systems; Row reduction and pivots https://wustl.zoom.us/rec/share/C27js1fQmPwxt-uvFb87RUP2AhbTtIVin8KI8VtZTir99oaJ0pf7tDfMo2jiQ0TT.q9THTcV1242vX49m 2020-09-14 Monday: Introduction and Octave basics https://wustl.zoom.us/rec/share/fJT9Kn0t7WVyc_0TsWq7TTzySb9MxL-3YvCe3x7pWH8f0IcfNXDhBae8JzLsNNoN.yF26EbBfF5a7Zyzr