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What does it mean to be linearly independent?

The vectors a 1, ..., a n are called linearly independent if there are no non-trivial combination of these vectors equal to the zero vector. That is, the vector a 1 , ..., a n are linearly independent if x 1 a 1 + ... + x n a n = 0 if and only if x 1 = 0, ..., x n = 0.

What does linearly dependent mean?

linearly dependent (Adjective) which has a nontrivial linear combination which is zero. see more »

What does linear independence mean?

Linear independence. by Marco Taboga, PhD. Linear independence is a central concept in linear algebra. Two or more vectors are said to be linearly independent if none of them can be written as a linear combination of the others. On the contrary, if at least one of them can be written as a linear combination of the others, then they are said to be linearly dependent.

Does linearly independent imply all elements are orthogonal?

linearly independent (Adjective) (Of a set of vectors or ring elements) whose nontrivial linear combinations are nonzero. Does linearly independent imply all elements are orthogonal? Vectors which are orthogonal to each other are linearly independent. But this does not imply that all linearly independent vectors are also orthogonal.


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