How to remove a certain row or column while using Eigen Library c++

Using the block functions is a bit cleaner:

void removeRow(Eigen::MatrixXd& matrix, unsigned int rowToRemove)
{
    unsigned int numRows = matrix.rows()-1;
    unsigned int numCols = matrix.cols();

    if( rowToRemove < numRows )
        matrix.block(rowToRemove,0,numRows-rowToRemove,numCols) = matrix.block(rowToRemove+1,0,numRows-rowToRemove,numCols);

    matrix.conservativeResize(numRows,numCols);
}

void removeColumn(Eigen::MatrixXd& matrix, unsigned int colToRemove)
{
    unsigned int numRows = matrix.rows();
    unsigned int numCols = matrix.cols()-1;

    if( colToRemove < numCols )
        matrix.block(0,colToRemove,numRows,numCols-colToRemove) = matrix.block(0,colToRemove+1,numRows,numCols-colToRemove);

    matrix.conservativeResize(numRows,numCols);
}

To improve Andrew's answer, use bottomRows/rightCols.

void removeRow(Eigen::MatrixXd& matrix, unsigned int rowToRemove)
{
    unsigned int numRows = matrix.rows()-1;
    unsigned int numCols = matrix.cols();

    if( rowToRemove < numRows )
        matrix.block(rowToRemove,0,numRows-rowToRemove,numCols) = matrix.bottomRows(numRows-rowToRemove);

    matrix.conservativeResize(numRows,numCols);
}

void removeColumn(Eigen::MatrixXd& matrix, unsigned int colToRemove)
{
    unsigned int numRows = matrix.rows();
    unsigned int numCols = matrix.cols()-1;

    if( colToRemove < numCols )
        matrix.block(0,colToRemove,numRows,numCols-colToRemove) = matrix.rightCols(numCols-colToRemove);

    matrix.conservativeResize(numRows,numCols);
}

You can do it a lot easier and shorter by using Eigen 3.3.0+(released 2016.08):

vector<int> indicesToKeep = vector<int>{ 1, 2, 3 };
VectorXi indicesToKeepVector = VectorXi(indicesToKeep.data(), indicesToKeep.size());
MatrixXf matrix = MatrixXf(); // your data should be here!
matrix = matrix(Eigen::placeholders::all, indicesToKeepVector); // select columns you want to keep(indicesToKeep), discard others
matrix = matrix(indicesToKeepVector, Eigen::placeholders::all); // select rows you want to keep(indicesToKeep), discard others
matrix = matrix(Eigen::seq(5, 10), Eigen::placeholders::all); // keep rows from 5 to 10
matrix = matrix(Eigen::placeholders::all, Eigen::seq(5, 10)); // keep columns from 5 to 10
matrix = matrix(Eigen::seqN(5, 5), Eigen::placeholders::all); // keep rows from 5 to 10
matrix = matrix(Eigen::placeholders::all, Eigen::seqN(5, 5)); // keep columns from 5 to 10