Column addition is a method used to add numbers by aligning them in columns according to their place values, starting from the rightmost digit and moving left. This technique emphasizes the importance of carrying over values when the sum of a column exceeds the base value, typically ten in base-10 arithmetic.
Linear independence is a fundamental concept in linear algebra that describes a set of vectors that do not linearly depend on each other, meaning no vector in the set can be written as a linear combination of the others. This property is crucial for determining the dimension of a vector space, as it ensures that the vectors span the space without redundancy.