Linear combinations, span, and basis vectors: Difference between revisions

Linear combinations, span, and basis vectors (view source)

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+A set B of vectors in a vector space V is called a '''basis''' if every element of V may be written in a unique way as a '''finite linear combination of elements''' of B.
+The coefficients of this linear combination are referred to as '''components or coordinates of the vector''' with respect to B.
+The elements of a basis are called '''basis vectors'''.
+Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.[1] In other words, a basis is a linearly independent spanning set.
+A vector space can have several bases; however all the bases have the same number of elements, called the dimension of the vector space.
+span
+basis of a vector
+linearly dependent
+linearly independent
 [[Category:Linear Algebra]]