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Author: rwieruch

.gitignore

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+node_modules

README.md

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 # Installation
 
-* `git clone [email protected]:rwieruch/node-babel-server.git`
-* `cd node-babel-server`
+* `git clone [email protected]:rwieruch/linear-algebra-matrix.git`
+* `cd linear-algebra-matrix`
 * `npm install`
 * `npm start`
-

index.js

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+import math from 'mathjs';
+
+// Matrices and Vectors
+
+const matrixA = math.matrix([[0, 1], [2, 3], [4, 5]]);
+const matrixB = math.matrix([[0], [1], [2]]);
+
+console.log(`Matrix A Dimension: ${matrixA.size()[0]}x${matrixA.size()[1]}`);
+console.log(`Is vector: ${matrixA.size()[1] === 1}`);
+
+console.log(`Matrix B Dimension: ${matrixB.size()[0]}x${matrixB.size()[1]}`);
+console.log(`Is vector: ${matrixB.size()[1] === 1}`);
+console.log('\n');
+
+// Matrix Addition
+
+const matrixC = math.matrix([[0, 1], [2, 3], [4, -5]]);
+const matrixD = math.matrix([[1, -1], [-2, 4], [-7, 4]]);
+
+const matrixAdditionCD = math.add(matrixC, matrixD);
+
+console.log('Matrix Addition:');
+console.log(matrixAdditionCD.valueOf());
+console.log('\n');
+
+// Matrix Subtraction
+
+const matrixE = math.matrix([[0, 1], [2, 3], [4, -5]]);
+const matrixF = math.matrix([[1, -1], [-2, 4], [-7, 4]]);
+
+const matrixAdditionEF = math.subtract(matrixE, matrixF);
+
+console.log('Matrix Subtraction:');
+console.log(matrixAdditionEF.valueOf());
+console.log('\n');
+
+// Matrix Scalar Multiplication
+
+const matrixG = math.matrix([[0, 1], [2, 3], [4, -5]]);
+
+const matrixG3 = math.multiply(3, matrixG);
+
+console.log('Matrix Scalar Multiplication:');
+console.log(matrixG3.valueOf());
+console.log('\n');
+
+// Matrix Scalar Division
+
+const matrixH = math.matrix([[2, 4], [6, 2], [4, -4]]);
+
+const matrixH2 = math.divide(matrixH, 2);
+
+console.log('Matrix Scalar Division:');
+console.log(matrixH2.valueOf());
+console.log('\n');
+
+// Matrix-Vector Multiplication
+
+const matrixI = math.matrix([[0, 1], [2, 3], [4, 5]]);
+const matrixJ = math.matrix([[2], [1]]);
+
+const matrixIJ = math.multiply(matrixI, matrixJ);
+
+console.log('Matrix-Vector Multiplication:');
+console.log(matrixIJ.valueOf());
+console.log('\n');
+
+// Matrix Multiplication
+
+const matrixK = math.matrix([[0, 1], [2, 3], [4, 5]]);
+const matrixL = math.matrix([[2, 4], [6, 2]]);
+
+const matrixKL = math.multiply(matrixK, matrixL);
+
+console.log('Matrix Multiplication:');
+console.log(matrixKL.valueOf());
+console.log('\n');
+
+// Matrix Property: Not Commutative
+
+const matrixN = math.matrix([[0, 1], [2, 3], [4, 5]]);
+const matrixO = math.matrix([[2, 4], [6, 2]]);
+
+const matrixNO = math.multiply(matrixN, matrixO);
+const matrixON = math.multiply(matrixO, matrixL);
+
+console.log('Are matrices commutative?');
+console.log(math.equal(matrixNO.size(), matrixON.size()));
+console.log('\n');
+
+// Matrix Property: But Associative
+
+const matrixP = math.matrix([[0, 1], [2, 3], [4, 5]]);
+const matrixQ = math.matrix([[2, 4], [6, 2]]);
+const matrixR = math.matrix([[5, 2], [2, -2]]);
+
+const matrixPQ_R = math.multiply(math.multiply(matrixP, matrixQ), matrixR);
+const matrixP_QR = math.multiply(matrixP, math.multiply(matrixQ, matrixR));
+
+console.log('Are matrices associative?');
+console.log(math.equal(matrixPQ_R.valueOf(), matrixP_QR.valueOf()));
+console.log('\n');
+
+// Identity (I) Matrix
+
+const matrixM = math.eye(3);
+
+console.log('Identity Matrix:');
+console.log(matrixM.valueOf());
+console.log('\n');
+
+// Inverse Matrix
+
+const matrixS = math.matrix([[0, 1], [2, 3]]);
+
+const matrixS_I = math.inv(matrixS);
+
+console.log('Inverse Matrix:');
+console.log(matrixS_I.valueOf());
+console.log('\n');
+
+// Calculated Inverse Matrix with Identity Matrix
+
+const matrixT = math.matrix([[0, 1], [2, 3]]);
+const matrixU = math.eye(2);
+
+const matrixT_I = math.divide(matrixU, matrixT);
+
+console.log('Calculated Inverse Matrix with Identity Matrix:');
+console.log(matrixT_I.valueOf());
+console.log('\n');
+
+// Transpose Matrix
+
+const matrixV = math.matrix([[0], [1], [2]]);
+
+const matrixV_T = math.transpose(matrixV);
+
+console.log('Transpose Matrix:');
+console.log(matrixV_T.valueOf());
+console.log('\n');
+
+// Example: Predicting Housing Prices with 3 competing Hypotheses
+
+console.log('Predicting Housing Prices with 3 competing Hypotheses:');
+console.log('const HOUSE_SIZES = [2104, 1416, 1534, 852];');
+console.log('const h1 = x => -40 + 0.25 * x;');
+console.log('const h2 = x => 200 + 0.1 * x;');
+console.log('const h3 = x => -150 + 0.4 * x;');
+console.log('\n');
+
+const houseSizeMatrix = math.matrix([
+  [1, 2104],
+  [1, 1416],
+  [1, 1534],
+  [1, 852],
+]);
+
+const hypothesesMatrix = math.matrix([
+  [-40, 200, -150],
+  [0.25, 0.1, 0.4],
+]);
+
+const competingResults = math.multiply(houseSizeMatrix, hypothesesMatrix);
+
+console.log('Column: Result for each Hypothesis');
+console.log('Row: Result for each House Size');
+console.log(competingResults.valueOf());
+console.log('\n');