122 \frametitle{Outline} |
122 \frametitle{Outline} |
123 \tableofcontents |
123 \tableofcontents |
124 % \pausesections |
124 % \pausesections |
125 \end{frame} |
125 \end{frame} |
126 |
126 |
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127 \section{Matrices} |
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128 |
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129 \begin{frame} |
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130 \frametitle{Matrices: Introduction} |
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131 We looked at the Van der Monde matrix in the previous session,\\ |
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132 let us now look at matrices in a little more detail. |
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133 \end{frame} |
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134 |
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135 \subsection{Initializing} |
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136 \begin{frame}[fragile] |
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137 \frametitle{Matrices: Initializing} |
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138 \begin{lstlisting} |
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139 In []: a = matrix([[1,2,3], |
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140 [4,5,6], |
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141 [7,8,9]]) |
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142 |
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143 In []: a |
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144 Out[]: |
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145 matrix([[1, 2, 3], |
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146 [4, 5, 6], |
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147 [7, 8, 9]]) |
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148 \end{lstlisting} |
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149 \end{frame} |
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150 |
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151 \subsection{Basic Operations} |
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152 \begin{frame}[fragile] |
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153 \frametitle{Inverse of a Matrix} |
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154 |
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155 \begin{small} |
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156 \begin{lstlisting} |
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157 In []: linalg.inv(A) |
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158 Out[]: |
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159 matrix([[ 0.07734807, 0.01657459, 0.32044199], |
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160 [ 0.09944751, -0.12154696, -0.01657459], |
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161 [-0.02762431, -0.07734807, 0.17127072]]) |
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162 |
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163 \end{lstlisting} |
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164 \end{small} |
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165 \end{frame} |
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166 |
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167 \begin{frame}[fragile] |
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168 \frametitle{Determinant} |
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169 \begin{lstlisting} |
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170 In []: linalg.det(a) |
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171 Out[]: -9.5171266700777579e-16 |
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172 \end{lstlisting} |
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173 \end{frame} |
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174 |
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175 \begin{frame}[fragile] |
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176 \frametitle{Computing Norms} |
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177 \begin{lstlisting} |
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178 In []: linalg.norm(a) |
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179 Out[]: 16.881943016134134 |
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180 \end{lstlisting} |
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181 \end{frame} |
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182 |
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183 \begin{frame}[fragile] |
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184 \frametitle{Eigen Values and Eigen Matrix} |
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185 \begin{small} |
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186 \begin{lstlisting} |
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187 In []: linalg.eigvals(a) |
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188 Out[]: array([1.61168440e+01, -1.11684397e+00, -1.22196337e-15]) |
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189 |
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190 In []: linalg.eig(a) |
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191 Out[]: |
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192 (array([ 1.61168440e+01, -1.11684397e+00, -1.22196337e-15]), |
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193 matrix([[-0.23197069, -0.78583024, 0.40824829], |
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194 [-0.52532209, -0.08675134, -0.81649658], |
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195 [-0.8186735 , 0.61232756, 0.40824829]])) |
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196 \end{lstlisting} |
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197 \end{small} |
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198 \end{frame} |
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199 |
127 \section{Solving linear equations} |
200 \section{Solving linear equations} |
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201 |
128 \begin{frame}[fragile] |
202 \begin{frame}[fragile] |
129 \frametitle{Solution of equations} |
203 \frametitle{Solution of equations} |
130 Consider, |
204 Consider, |
131 \begin{align*} |
205 \begin{align*} |
132 3x + 2y - z & = 1 \\ |
206 3x + 2y - z & = 1 \\ |
168 matrix([[ 1.00000000e+00], |
242 matrix([[ 1.00000000e+00], |
169 [ -2.00000000e+00], |
243 [ -2.00000000e+00], |
170 [ 2.22044605e-16]]) |
244 [ 2.22044605e-16]]) |
171 \end{lstlisting} |
245 \end{lstlisting} |
172 \end{frame} |
246 \end{frame} |
173 |
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174 \section{Matrices} |
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175 \subsection{Initializing} |
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176 \begin{frame}[fragile] |
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177 \frametitle{Matrices: Initializing} |
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178 \begin{lstlisting} |
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179 In []: a = matrix([[1,2,3], |
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180 [4,5,6], |
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181 [7,8,9]]) |
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182 |
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183 In []: a |
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184 Out[]: |
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185 matrix([[1, 2, 3], |
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186 [4, 5, 6], |
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187 [7, 8, 9]]) |
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188 \end{lstlisting} |
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189 \end{frame} |
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190 |
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191 \subsection{Basic Operations} |
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192 \begin{frame}[fragile] |
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193 \frametitle{Inverse of a Matrix} |
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194 |
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195 \begin{small} |
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196 \begin{lstlisting} |
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197 In []: linalg.inv(A) |
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198 Out[]: |
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199 matrix([[ 0.07734807, 0.01657459, 0.32044199], |
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200 [ 0.09944751, -0.12154696, -0.01657459], |
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201 [-0.02762431, -0.07734807, 0.17127072]]) |
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202 |
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203 \end{lstlisting} |
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204 \end{small} |
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205 \end{frame} |
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206 |
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207 \begin{frame}[fragile] |
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208 \frametitle{Determinant} |
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209 \begin{lstlisting} |
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210 In []: linalg.det(a) |
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211 Out[]: -9.5171266700777579e-16 |
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212 \end{lstlisting} |
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213 \end{frame} |
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214 |
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215 \begin{frame}[fragile] |
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216 \frametitle{Computing Norms} |
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217 \begin{lstlisting} |
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218 In []: linalg.norm(a) |
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219 Out[]: 16.881943016134134 |
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220 \end{lstlisting} |
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221 \end{frame} |
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222 |
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223 \begin{frame}[fragile] |
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224 \frametitle{Eigen Values and Eigen Matrix} |
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225 \begin{small} |
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226 \begin{lstlisting} |
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227 In []: linalg.eigvals(a) |
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228 Out[]: array([1.61168440e+01, -1.11684397e+00, -1.22196337e-15]) |
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229 |
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230 In []: linalg.eig(a) |
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231 Out[]: |
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232 (array([ 1.61168440e+01, -1.11684397e+00, -1.22196337e-15]), |
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233 matrix([[-0.23197069, -0.78583024, 0.40824829], |
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234 [-0.52532209, -0.08675134, -0.81649658], |
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235 [-0.8186735 , 0.61232756, 0.40824829]])) |
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236 \end{lstlisting} |
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237 \end{small} |
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238 \end{frame} |
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239 |
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240 |
247 |
241 \section{Integration} |
248 \section{Integration} |
242 |
249 |
243 \subsection{Quadrature} |
250 \subsection{Quadrature} |
244 |
251 |