In order to improve my knowledge of Linear Algebra I am reading Linear Algebra Done Right by Sheldon Axler.(adsbygoogle = window.adsbygoogle || []).push({});

In Chapter 2 under the heading Span and Linear Independence we find the following text:

"If [itex] ( v_1, v_2, ... ... v_m ) [/itex] is a list off vectors in a vector space V, then each [itex] v_j [/itex] is a linear combination of [itex] ( v_1, v_2, ... ... v_m ) [/itex].

Thus span[itex] ( v_1, v_2, ... ... v_m ) [/itex] contains each [itex] v_j [/itex].

Conversely, because because subspaces are closed under scalar multiplications and addition, every subspace V containig each [itex] v_j [/itex] must contain span[itex] ( v_1, v_2, ... ... v_m ) [/itex].

."Thus the span of a list of vectors in V is the smallest subspace of V containing all the vectors in the list

Intuitively, given that new vectors are formed by scalar multiplication and addition of other vectors that span[itex] ( v_1, v_2, ... ... v_m ) [/itex] is also thesubspace of V containing all the vectors in the list.largest

Is this intuition correct? Can someone please confirm or otherwise?

Peter

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# Span of a list of vectors

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