2b:null 2c:["$","title",null,{"children":"Linear Algebra | Feng Yifei | Observable"}] 31:T4c1,{ const generator = Algebra(2, 0, 1).inline(() => { var point = (x, y) => 1e12 - x * 1e02 + y * 1e01; // Similarly, we can define lines directly. The euclidean line ax + by + c can be specified so : var line = (a, b, c) => a * 1e1 + b * 1e2 + c * 1e0; // Define 3 points. var A = point(-1, 1), B = point(-1, -1), C = point(1, -1); // Define the line y=x-0.5 var L = line(-1, 1, 0.5); // Or by joining two points. We define M as a function so it will update when C or A are dragged. var M = () => C & A; // Points can also be found by intersecting two lines. We similarly define D as a function for interactive updates. var D = () => L ^ M; return this.graph( [ A, 'A', B, 'B', C, 'C', L, 'L', M, 'M', D, 'D', 0xffcccc, // Set the color light red. [B, C], // Render line segment from B to C. 0xffcccc, // Set the color to light red. [A, B, C] // render polygon ABC. ], { grid: true } ); }); const element = generator(); // HTML Element element.style.width = width; // Style return element; }32:T4ac,{ const tr = math.matrix(T); const multiply = math.multiply(origin2M, tr); const result = multiply['_data']; const inline = ({ target, origin2D, result }) => { target.origin2D = origin2D; target.result = result; return () => { const point = (x, y) => 1e12 - x * 1e02 - y * 1e01; const Z = point(0, 0); const O1 = point(this.origin2D[0][0], this.origin2D[1][0]); const O2 = point(this.origin2D[0][1], this.origin2D[1][1]); const T1 = point(this.result[0][0], this.result[1][0]); const T2 = point(this.result[0][1], this.result[1][1]); return this.graph( [ 0x6915cf, Z, '(0, 0)', 0x8bbabb, O1, '(O11, O21)', O2, '(O21, O22)', [Z, O1], [Z, O2], 0xff7315, T1, '(T11, T21)', T2, '(T21, T22)', [Z, T1], [Z, T2] ], { grid: true } ); }; }; const target = Algebra(2, 0, 1); const generator = target.inline(inline({ target, origin2D, result })); const element = generator(); element.style.width = width; return element; }33:T7b5,{ const inline = ({ target, vector }, matrix = {}) => { target.vector = vector; target.matrix = matrix; target.transform = (v, matrix) => { let result = v; if (matrix.scale !== undefined) { result = math.multiply(math.matrix(matrix.scale), math.matrix(v)); } if (matrix.rotation !== undefined) { result = math.multiply(math.matrix(matrix.rotation), result); } const p = result['_data']; return { x: p[0][0], y: p[1][0] }; }; return () => { const point = (x, y) => 1e12 - x * 1e02 - y * 1e01; const line = (a, b, c) => a * 1e1 + b * 1e2 + c * 1e0; const BaseX = line(0, 1, 0); const BaseY = line(1, 0, 0); const Z = point(0, 0); const X = point(1, 0); const Y = point(0, 1); const O = point(this.vector[0][0], this.vector[1][0]); const txm = this.transform([[1], [0]], this.matrix); const TX = point(txm.x, txm.y); const tym = this.transform([[0], [1]], this.matrix); const TY = point(tym.x, tym.y); const tvm = this.transform(this.vector, this.matrix); const TV = point(tvm.x, tvm.y); return this.graph( [ 0x000000, BaseX, 'X', BaseY, 'Y', Z, '(0, 0)', 0xe47312, X, '(1, 0)', [Z, X], Y, '(0, 1)', [Z, Y], 0xe3b04b, O, 'Vector', [Z, O], 0x3e64ff, TX, '(1, 0)', [Z, TX], TY, '(0, 1)', [Z, TY], 0x6807f9, TV, 'Transformed', [Z, TV] ], { grid: true } ); }; }; const target = Algebra(2, 0, 1); const generator = target.inline( inline({ target, vector }, { scale, rotation }) ); const element = generator(); element.style.width = width; return element; 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2f:{"id":"d8fe53eff33145f8","slug":"linear-algebra","title":"Linear Algebra","thumbnail":"b8ebe3c022584941df66160046718dee6b33f2a4d7cfa128fdd6aad748c273b2","access_level":"public","create_time":"$D2019-12-09T10:23:28.426Z","update_time":"$D2019-12-29T06:26:27.842Z","view_time":null,"first_public_time":"$D2019-12-09T11:11:45.202Z","fork":false,"stars":3,"starred":false,"owner":{"type":"team","id":"2a278c3908e45a90","login":"fengyfei","name":"Feng Yifei","avatar_url":"https://avatars-next.observableusercontent.com/c5b93e151f999a0d3ae3ddc3285ea44aaaaf234cd045885cc92d8c1d0a529148","tier":"starter_2024"},"version":437,"publish_version":437,"role":null,"authored":false,"authors":[{"type":"individual","id":"582cdf51952494b0","login":"fengyfei","name":"Feng Yifei","avatar_url":"https://avatars-next.observableusercontent.com/c5b93e151f999a0d3ae3ddc3285ea44aaaaf234cd045885cc92d8c1d0a529148","tier":null}],"members":[{"type":"individual","id":"582cdf51952494b0","login":"fengyfei","name":"Feng Yifei","avatar_url":"https://avatars-next.observableusercontent.com/c5b93e151f999a0d3ae3ddc3285ea44aaaaf234cd045885cc92d8c1d0a529148","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":2,"collection":{"id":"714d03c41859e603","slug":"math","title":"Math","owner":{"id":"2a278c3908e45a90","login":"fengyfei","name":"Feng Yifei"}},"type":"notebook","body":{"title":"Linear Algebra","cells":[{"id":0,"value":"md`# Linear Algebra`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":6,"value":"md`\n## References\n- [ganja.js](https://github.com/enkimute/ganja.js): Geometric Algebra for javascript.\n- [Linear Algebra JS](https://rohan-sawhney.github.io/linear-algebra-js/)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":40,"value":"md`\n## Training\n### Ganja Cheat Sheet\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":418,"value":"PGA2DCheat = FileAttachment('2DPGA.png').image()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":422,"value":"PGA3DCheatP1 = FileAttachment('3DPGA@1.png').image()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":426,"value":"PGA3DCheatP2 = FileAttachment('3DPGA@2.png').image()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":430,"value":"md`\n### Ganja Quick Start Template\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":46,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":91,"value":"md `\n## Linear Algebra Basics\n### Matrix\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":146,"value":"origin2D = [[1, 0], [0, 1]]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":113,"value":"origin2M = math.matrix(origin2D)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":109,"value":"tex`${matrixTexFormat(origin2D)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":118,"value":"viewof T = {\n const form = html`\n \n `;\n\n form.oninput = () =>\n (form.value = [\n [form.T11.valueAsNumber, form.T12.valueAsNumber],\n [form.T21.valueAsNumber, form.T22.valueAsNumber]\n ]);\n\n form.oninput();\n\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":127,"value":"{\n const tr = math.matrix(T);\n const multiply = tex`\n ${matrixTexFormat(tr)} \\cdot ${matrixTexFormat(\n origin2M\n )} = ${matrixTexFormat(math.multiply(origin2M, tr))}\n`;\n\n return multiply;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":249,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":332,"value":"md`\n### Transform\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":335,"value":"viewof vector = {\n const form = html`\n \n `;\n\n form.oninput = () =>\n (form.value = [[form.X.valueAsNumber], [form.Y.valueAsNumber]]);\n\n form.oninput();\n\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":342,"value":"tex`${matrixTexFormat(vector)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":381,"value":"viewof scale = {\n const form = html`\n \n `;\n\n form.oninput = () =>\n (form.value = [[form.X.valueAsNumber, 0], [0, form.Y.valueAsNumber]]);\n\n form.oninput();\n\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":403,"value":"tex`${matrixTexFormat(scale)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":407,"value":"viewof rotation = {\n const form = html`\n \n `;\n\n form.oninput = () => {\n const angle = form.A.valueAsNumber;\n const radian = (Math.PI * angle) / 180.0;\n\n form.value = [\n [Math.cos(radian), -Math.sin(radian)],\n [Math.sin(radian), Math.cos(radian)]\n ];\n };\n\n form.oninput();\n\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":412,"value":"tex`${matrixTexFormat(rotation)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":346,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":11,"value":"md `\n## Imports\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":106,"value":"import { matrixTexFormat } from '@fengyfei/mathematics'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":12,"value":"Algebra=require('ganja.js')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":97,"value":"math = require('mathjs')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W34","stdlib":"1","titling":"auto"}} 30:"$2f:body"