4x4 Matrix Multiplication Calculator

Matrix Multiplication Formula:

\[ (A B)_{ij} = \sum_k A_{ik} B_{kj} \text{ for 4x4 matrices} \]

Matrix A

Matrix B

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1. What is 4x4 Matrix Multiplication?

Matrix multiplication is a binary operation that produces a matrix from two matrices. For 4x4 matrices, each element in the resulting matrix is computed as the dot product of the corresponding row from the first matrix and column from the second matrix.

2. How Does the Calculator Work?

The calculator uses the standard matrix multiplication formula:

\[ (A B)_{ij} = \sum_{k=1}^4 A_{ik} B_{kj} \]

Where:

\( A \) — First 4x4 matrix
\( B \) — Second 4x4 matrix
\( (AB)_{ij} \) — Element at row i, column j of the product matrix

3. Applications of Matrix Multiplication

Details: 4x4 matrix multiplication is fundamental in computer graphics (3D transformations), physics simulations, engineering calculations, and solving systems of linear equations.

4. Using the Calculator

Tips: Enter numerical values for all elements in both matrices. The calculator will compute the product matrix element by element.

5. Frequently Asked Questions (FAQ)

Q1: What are the requirements for matrix multiplication?
A: The number of columns in the first matrix must equal the number of rows in the second matrix. For 4x4 matrices, this is automatically satisfied.

Q2: Is matrix multiplication commutative?
A: No, in general AB ≠ BA for matrices. The order of multiplication matters.

Q3: What's the time complexity of 4x4 matrix multiplication?
A: O(n³) for n×n matrices, so O(64) operations for 4x4 matrices.

Q4: Can I multiply matrices of different sizes?
A: This calculator is specifically for 4x4 matrices. For other sizes, the number of columns in A must match rows in B.

Q5: What about scalar multiplication?
A: This calculator performs matrix multiplication, not scalar multiplication (which multiplies each element by a single number).