row rank मीनिंग इन हिंदी

Imposing any desired value of the state vector \ textbf { x } ( n ) on the left side, this can always be solved for the stacked vector of control vectors if and only if the matrix of matrices at the beginning of the right side has full row rank.
The column rank of a matrix is the dimension of the right module generated by the columns, and the row rank is dimension of the left module generated by the rows; the same proof as for the vector space case can be used to show that these ranks are the same, and define the rank of a matrix.
A fundamental result in linear algebra is that the column rank and the row rank are always equal . ( Two proofs of this result are given in below . ) This number ( i . e ., the number of linearly independent rows or columns ) is simply called the "'rank "'of " A ".
For the cases where has full row or column rank, and the inverse of the correlation matrix ( AA ^ * for with full row rank or A ^ * A for full column rank ) is already known, the pseudoinverse for matrices related to A can be computed by applying the Sherman Morrison Woodbury formula to update the inverse of the correlation matrix, which may need less work.
Indeed, since the column vectors of " A " are the row vectors of the transpose of " A ", the statement that the column rank of a matrix equals its row rank is equivalent to the statement that the rank of a matrix is equal to the rank of its transpose, i . e ., rk ( " A " ) = rk ( " A"