Full linear algebra for the ai

#include <iostream>
#include <math.h>
#include <string>
#include <vector>
#include <cstdlib>

using namespace std;

vector<vector<float>> transpose(vector<vector<float>> input){
    float input_rows = input.size();
    float input_cols = input[0].size();
    vector<vector<float>> output (input_cols, vector<float>(input_rows));
    for(short i = 0; i < input_rows;){
        for(short k = 0; k < input_cols;){
            output[k][i] = input[i][k];
            ++k;
        }
        ++i;
    }
    return output;
}

vector<vector<float>> dotProduct (vector<vector<float>> inputs, vector<vector<float>> weights, vector<float> biases) {
    short col_count = inputs.size();
    vector<vector<float>> output (col_count);
    for(short i = 0; i < col_count; ++i){
        short row_count = inputs[i].size();
        output[i].resize(row_count);
        for(short k = 0; k < row_count; ++k){
            output[i][k] = inputs[i][k] * weights[i][k] + biases[i];
        }
    }
    return output;
}

vector<vector<float>> full_dot(vector<vector<float>> inputs, vector<vector<float>> weights, vector<float> biases) {
    return dotProduct(inputs, transpose(weights), biases);
}

int main() {
    vector<vector<float>> inputs {
        {1.2, 3.5, 0.6, 0.91},
        {4.3, 2.1, 1.9, 0.13},
        {1.9, 1.2, 4.0, 0.20}
                                 };
    vector<vector<float>> weights {
        {2, 4, 6.8, 1.3},
        {3.4, 1.2, 3., 2.1},
        {4.1, 5.3, 0.9, .12}
    };
    vector<float> biases {
        1.2, 3, 0.1, 2.1
    };

    vector<vector<float>> output = full_dot(inputs, weights, biases);

    for(char j; j < output.size(); ++j) {
        for(char k; k < output[j].size(); ++k){
            cout << output[j][k] << endl;
        }
    }

    return 0;
}