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45:["$","title",null,{"children":"Linear Algebra Scratchpad | Andrew Lee | Observable"}] 4d:T92f,svg``4e:[] 49:{"id":"cbdd7298bd19d736","slug":"linear-algebra-scratchpad","title":"Linear Algebra Scratchpad","thumbnail":"0dbab99b7e7aca2c388ad058d314d13a574d081e82bcc6610d75df8e7595e739","access_level":"public","create_time":"$D2018-04-12T13:12:12.280Z","update_time":"$D2018-04-16T21:44:10.092Z","view_time":null,"first_public_time":"$D2018-04-12T14:01:06.099Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"e6fabc34f6550ebe","login":"vndrewlee","name":"Andrew Lee","avatar_url":"https://avatars-next.observableusercontent.com/edab37df6e3107a11e9652c058598afe54f8ae162435add85932835d5823545a","tier":"starter_2024","bio":"product manager at glean.io","followed_by_you":false,"follows_you":false},"version":203,"publish_version":203,"role":null,"authored":false,"authors":[{"type":"individual","id":"29eb280aae078328","login":"vndrewlee","name":"Andrew Lee","avatar_url":"https://avatars-next.observableusercontent.com/edab37df6e3107a11e9652c058598afe54f8ae162435add85932835d5823545a","tier":null,"bio":"product manager at glean.io","followed_by_you":false,"follows_you":false}],"members":[{"type":"individual","id":"29eb280aae078328","login":"vndrewlee","name":"Andrew Lee","avatar_url":"https://avatars-next.observableusercontent.com/edab37df6e3107a11e9652c058598afe54f8ae162435add85932835d5823545a","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Linear Algebra Scratchpad","cells":[{"id":0,"value":"md`# Linear Algebra Scratchpad`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":65,"value":"md`Using Tensorflow.js to help us with the maths`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"tf = require('@tensorflow/tfjs')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":149,"value":"md`## Vectors (please bear with me)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"md`Vectors are a new thing, similar to co-ordinates, but with *magnitude* and *direction*. \n\nThey are relative measures.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":153,"value":"$4d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":67,"value":"md`Define example vectors to work with`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"vector_a = tf.tensor1d([2,2])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"vector_b = tf.tensor1d([4,1])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":69,"value":"md`## We can do familiar operations, such as addition, subtraction, etc.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":110,"value":"md`These operations happen pairwise`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":72,"value":"tf.add(vector_a, vector_b).data()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":83,"value":"tf.sub(vector_a, vector_b).data()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":163,"value":"md`Our example vectors are setup with 2 dimensions, but there is no limit to the number of dimensions. The operations work on any length / size.\n\nThe term *n-dimensional* refers to the fact that the number of dimensions is arbitrary.\n\nTry changing the length of our vectors and seeing what happens.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":91,"value":"md`## Importantly, geometry also works`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":96,"value":"md`\nMost linear algebra libraries also have helper functions to do this stuff.\n\nWe can use the Pythagorean theorem to get distances between vectors.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":99,"value":"tex`a^2 + b^2 = c^2`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":103,"value":"vector_a.norm().data()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":114,"value":"md`Let's verify that number`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"// 2^2 + 2^2 = c^2\n// c^2 = 4 + 4\n// c = 8^.5\n\n8**.5","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":173,"value":"md`We can use the same process to get a distance between vectors.` ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":90,"value":"tf.sub(vector_a, vector_b).norm().data()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":194,"value":"md`## Shapes`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":197,"value":"md`You'll often hear people describing shapes in n-dimensional space (also sometimes called hyperspace (*pew! pew!*).\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":200,"value":"html` $\"made$ `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":202,"value":"md`But seriously, what does that mean?`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"md`## Math part done!`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4e","stdlib":"1"}} 44:null