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My prof introduced a concept that required use of a vector, which he represented as follows (imagine there is only one pair of brackets below, tall enough to encapsulate both terms; I don't have the rep to paste an image and don't know how to format this otherwise):

v =

[-1/2]

[1/2 ]

One of my personal weaknesses is a lack of familiarity with mathematical notation. Is there an accepted way of interpreting this kind notation? Does it vary by discipline, or is this something generalizable that I really should know? Is there something intrinsic about this notation that would lead one to interpret it differently than if it were written v = [-1/4, 1/4]?

Thanks for the help!

Adam
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    I'm voting to close this question as off-topic because it's about mathematics, not programming or software development. – Pang Sep 25 '15 at 01:38

2 Answers2

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A vector is a one-dimensional matrix, but it is a matrix nonetheless. Writing it out horizontally instead of vertically or vice versa changes the dimensionality of the matrix, changing its meaning among the rest of the equations.

Ignacio Vazquez-Abrams
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Very often you will "transform" a vector by multiplying them by a matrix. For instance, to rotate a vector, you have to multiply it by the rotation matrix, etc. If your vectors are codified in columns, a multiplication by a matrix M will act from the left, M * v, because of the way the multiplication works (every row of M by the column vector v.) Alternatively, if your vectors are codified as rows (v = [-1/4, 1/4]) the multiplication will act from the right: v * M, again, because of the "row by column" definition of the multiplication of "matrices".

So, it is up to you to represent vectors as rows or columns provided your convention is consistent with the way you multiply them by matrices.

Leandro Caniglia
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