Rank of a matrix

The rank of a matrix is a measure of the number of independent pieces of information it contains. It tells us how many unique directions or dimensions are represented by the matrix's data. For example, in a system of equations, the rank indicates how many equations provide distinct, useful information. A higher rank means more independent data, while a lower rank suggests some information is redundant or dependent. Essentially, the rank helps us understand the complexity, structure, and solvability of the data or system represented by the matrix.