I am trying to implement an algorithm requiring matrix multiplication. I know I can program this in the rudimentary way similar to doing the process by hand, but I am worried about the computational costs associated with this.

In solidity, the "matrix" would just be a two-dimensional array or even just a vector.

Does anyone know of an existing implementation of matrix multiplication in solidity? I want to make sure I do this efficiently and am wondering if anyone else has established a good way of doing it. I am unable to find any library or posts on the subject.

Thanks in advance.

  • You might have to go with a counter-intuitive approach to complete it with O(1) complexity. How big is the matrix? How often does it change? What makes it change? What is it for? A general-purpose approach is probably out of the question, so more insight into the specific requirements might help pinpoint a suitable method for you. Jun 10, 2019 at 15:05
  • Thanks, the matrices multiplied will not be huge. Say, 10x10 or less. Matrix multiplication will be done very frequently. In particular, the multiplication being done will be a square matrix by a vector. The square matrix will not change, but the vector will change every time. I am doing this to implement a decentralized consensus algorithm on the blockchain, where each node queries the smart contract to receive their next state.
    – user51707
    Jun 10, 2019 at 15:23
  • That's encouraging. Writes are considerably more expensive than reads so it is good news that the 10x10 structure is static. Where does the vector come from? How does it evolve? I imagine it is computed deterministically somehow? Jun 10, 2019 at 15:31
  • Yes, it is. I believe I have a "good enough" solution that I will work with for now as long as I know the array sizes. Thank you for your answer and help.
    – user51707
    Jun 10, 2019 at 16:01

1 Answer 1


This simple method is what I will use for now as long as I know the dimensions of the matrices. Thanks.

function mat3Mult(uint[3][3] mat1, uint[3][3] mat2) private returns (uint[3][3]) { // multiplies 3x3 matrix with 3x3 matrix
        uint r1 = mat1.length; // rows of mat1
        uint c1 = mat1[0].length; // columns of mat1
        uint c2 = mat2[0].length; // columns of mat2

        uint[3][3] memory result; 

        for(uint i = 0; i < r1; ++i) {
            for(uint j = 0; j < c2; ++j) {
                for(uint k = 0; k < c1; ++k) {
                    result[i][j] += mat1[i][k] * mat2[k][j];


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