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Definition: A set of vectors that is not linearly dependent. We say that matrices A_1, A_2, … , A_k of the same size are linearly independent if the only solution of the equation (c_1)A_1 + (c_2)A_2 + ... + (c_k)A_k = O is the trivial one: c_1 = c_2 = ... = 0.
Source: Linear Algebra: A Modern Introduction, 3rd edition by David Poole (note-custom edition titled Matrix Algebra)