Matrix Multiplication Calculator
Define Matrix Dimensions
Enter Matrix Elements
Matrix A
Matrix B
Resulting Matrix (A × B)
Matrix A (' + matrixARows + 'x' + matrixACols + ')
'; matrixBInputsDiv.innerHTML = 'Matrix B (' + matrixBRows + 'x' + matrixBCols + ')
'; // Generate Matrix A inputs for (var i = 0; i < matrixARows; i++) { var rowDiv = document.createElement("div"); rowDiv.style.display = "flex"; rowDiv.style.marginBottom = "5px"; for (var j = 0; j < matrixACols; j++) { var input = document.createElement("input"); input.type = "number"; input.id = "matrixA_" + i + "_" + j; input.value = "0"; // Default value input.style.width = "50px"; input.style.padding = "5px"; input.style.margin = "2px"; input.style.border = "1px solid #ccc"; input.style.borderRadius = "3px"; rowDiv.appendChild(input); } matrixAInputsDiv.appendChild(rowDiv); } // Generate Matrix B inputs for (var i = 0; i < matrixBRows; i++) { var rowDiv = document.createElement("div"); rowDiv.style.display = "flex"; rowDiv.style.marginBottom = "5px"; for (var j = 0; j < matrixBCols; j++) { var input = document.createElement("input"); input.type = "number"; input.id = "matrixB_" + i + "_" + j; input.value = "0"; // Default value input.style.width = "50px"; input.style.padding = "5px"; input.style.margin = "2px"; input.style.border = "1px solid #ccc"; input.style.borderRadius = "3px"; rowDiv.appendChild(input); } matrixBInputsDiv.appendChild(rowDiv); } document.getElementById("matrixInputArea").style.display = "block"; } function calculateMatrixProduct() { var matrixARows = parseInt(document.getElementById("matrixARows").value); var matrixACols = parseInt(document.getElementById("matrixACols").value); var matrixBRows = parseInt(document.getElementById("matrixBRows").value); var matrixBCols = parseInt(document.getElementById("matrixBCols").value); var errorMessageDiv = document.getElementById("errorMessage"); errorMessageDiv.innerHTML = ""; document.getElementById("matrixResult").style.display = "none"; document.getElementById("resultMatrixDisplay").innerHTML = ""; if (isNaN(matrixARows) || isNaN(matrixACols) || isNaN(matrixBRows) || isNaN(matrixBCols) || matrixARows <= 0 || matrixACols <= 0 || matrixBRows <= 0 || matrixBCols <= 0) { errorMessageDiv.innerHTML = "Please generate matrices with valid dimensions first."; return; } if (matrixACols !== matrixBRows) { errorMessageDiv.innerHTML = "Matrix multiplication is not possible. The number of columns in Matrix A must equal the number of rows in Matrix B."; return; } var matrixA = []; for (var i = 0; i < matrixARows; i++) { matrixA[i] = []; for (var j = 0; j < matrixACols; j++) { var inputElement = document.getElementById("matrixA_" + i + "_" + j); var value = parseFloat(inputElement.value); if (isNaN(value)) { errorMessageDiv.innerHTML = "Please enter valid numbers for all elements in Matrix A."; return; } matrixA[i][j] = value; } } var matrixB = []; for (var i = 0; i < matrixBRows; i++) { matrixB[i] = []; for (var j = 0; j < matrixBCols; j++) { var inputElement = document.getElementById("matrixB_" + i + "_" + j); var value = parseFloat(inputElement.value); if (isNaN(value)) { errorMessageDiv.innerHTML = "Please enter valid numbers for all elements in Matrix B."; return; } matrixB[i][j] = value; } } var resultMatrix = []; for (var i = 0; i < matrixARows; i++) { resultMatrix[i] = []; for (var j = 0; j < matrixBCols; j++) { var sum = 0; for (var k = 0; k < matrixACols; k++) { // or matrixBRows, they are equal sum += matrixA[i][k] * matrixB[k][j]; } resultMatrix[i][j] = sum; } } displayResultMatrix(resultMatrix); } function displayResultMatrix(matrix) { var resultMatrixDisplayDiv = document.getElementById("resultMatrixDisplay"); var table = '| ' + matrix[i][j].toFixed(2) + ' | '; } table += '
Understanding Matrix Multiplication
Matrix multiplication is a fundamental operation in linear algebra with wide-ranging applications across various fields, including computer graphics, physics, engineering, economics, and machine learning. Unlike scalar multiplication (where you multiply each element by a single number), matrix multiplication involves a more complex process that combines rows from the first matrix with columns from the second matrix.
What is a Matrix?
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. For example, a 2×3 matrix has 2 rows and 3 columns:
A = [[a11, a12, a13],
[a21, a22, a23]]
The Rules of Matrix Multiplication
For two matrices, A and B, to be multiplied to form a product matrix C (i.e., C = A × B), a crucial condition must be met:
- Compatibility Rule: The number of columns in the first matrix (A) must be equal to the number of rows in the second matrix (B).
If matrix A has dimensions (m × n) and matrix B has dimensions (n × p), then the resulting product matrix C will have dimensions (m × p). Notice that the 'n' (columns of A and rows of B) must match, and it disappears in the result's dimensions.
How to Perform Matrix Multiplication
Each element Cij in the product matrix C is calculated by taking the dot product of the i-th row of matrix A and the j-th column of matrix B. This means you multiply corresponding elements from the row and column and then sum those products.
Let's consider two matrices:
Matrix A (2x2): Matrix B (2x2):
[[a11, a12], [[b11, b12],
[a21, a22]] [b21, b22]]
The product matrix C (2×2) would be:
C = [[(a11*b11 + a12*b21), (a11*b12 + a12*b22)],
[(a21*b11 + a22*b21), (a21*b12 + a22*b22)]]
Example Calculation
Let's use the default values provided in the calculator:
Matrix A: [[1, 2],
[3, 4]]
Matrix B: [[5, 6],
[7, 8]]
Here, Matrix A is 2×2 and Matrix B is 2×2. Since the columns of A (2) equal the rows of B (2), multiplication is possible, and the result will be a 2×2 matrix.
Calculating each element of the product matrix C:
- C11 = (1 * 5) + (2 * 7) = 5 + 14 = 19
- C12 = (1 * 6) + (2 * 8) = 6 + 16 = 22
- C21 = (3 * 5) + (4 * 7) = 15 + 28 = 43
- C22 = (3 * 6) + (4 * 8) = 18 + 32 = 50
So, the resulting matrix C is:
C = [[19, 22],
[43, 50]]
How to Use the Matrix Multiplication Calculator
- Define Dimensions: Enter the number of rows and columns for Matrix A and Matrix B in the respective input fields.
- Generate Input Fields: Click the "Generate Matrix Input Fields" button. The calculator will check for compatibility and then display input boxes for each element of your matrices.
- Enter Elements: Fill in the numerical values for each element in Matrix A and Matrix B.
- Calculate Product: Click the "Calculate Matrix Product" button. The resulting product matrix will be displayed below.
- Error Handling: If the dimensions are incompatible or if you enter non-numeric values, an error message will appear.
This calculator simplifies the often tedious process of manual matrix multiplication, allowing you to quickly verify your calculations or explore different matrix operations.