The rank of a matrix is the dimension of the vector space generated by its rows or columns, indicating the maximum number of linearly independent row or column vectors in the matrix. It provides crucial information about the solutions of linear systems, including whether the system has a unique solution, infinitely many solutions, or no solution at all.

Matrix Rank

The rank of a matrix is the dimension of the vector space spanned by its rows or columns, indicating the maximum number of linearly independent row or column vectors in the matrix. It provides crucial insights into the matrix's properties, such as its invertibility, solutions to linear equations, and the dimensionality of its image and kernel.

rank of a matrix

dimension of the vector space

vector space generated by its rows

Vector space generated by its columns

Linearly independent row vectors

Linearly independent column vectors

Maximum number of linearly independent vectors

solutions of linear systems

unique solution

infinitely many solutions

no solution at all

Singular Value Decomposition

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