Linearly independent but not orthogonal, how come? - Physics …
Jul 16, 2008 · Vectors which are orthogonal to each other are linearly independent. But this does not imply that all linearly independent vectors are also orthogonal. Take i+j for example. The …
Checking the linear independence of elements of 2 X 2 matrices
Aug 13, 2018 · Another way is to use the definition of linear independence. The matrices A, B, and C (which you are calling |1>, |2>, and |3>) are linearly independent if there is only the …
Characterizing linear independence in terms of span
Mar 2, 2025 · Add one non-zero vector to such a set and it isn't linearly independent anymore, which in return automatically generates a linear expression in terms of basis vectors.
Linear independence of sin (x), cos (x) and 1, proof
Apr 23, 2012 · It does if we want to prove the linear independence (because of the definition itself). I'm worried about the fact that not all x satisfy the conditions sin (x)\neq 0, cos (x)\neq 0 …
How to prove the linear indenpendency of an infinite set
Dec 1, 2011 · If one knows linear independence for finite sets, then you can easily extent it to infinite sets: An infinite set is linear independent if all its finite subsets are linear independent.
Linear Independence of Vectors: Why Determinant ≠ 0?
Apr 29, 2013 · If you put your vectors in a matrix, you get a linear function identified by the matrix. If you can "reach" all of $\mathbb R^3$ with this function, your vectors are linearly independent.
Linear Independence of 3 Vectors in R^4 - Physics Forums
Oct 9, 2006 · LINEAR ALGEBRA: 3 vecotrs in R^4 (with 6 variables) -- Are they linearly independent? For which values of the constants a, b, c, d, e, anf f are the following vectors …
Linear Independence: Showing 1, sin^2(x), sin(2x) is Independent
Sep 28, 2011 · New axis of rotation for composite of rotations in Euclidean space Jun 5, 2025 Replies 4 Views 1K Linear independence of Coordinate vectors as columns & rows Dec 21, …
Linear independence of orthogonal and orthonormal sets?
Apr 20, 2010 · What's the deal? I thought orthogonality => linear independence. I know if the statement was the other way around then it would be false, since Linear independence =/> …
Are These Vectors Linearly Independent? - Physics Forums
Sep 10, 2012 · Homework Statement Let S={r,u,d,x} be a set of vectors. If x=4r+4u+4d, determine whether or not the four vectors listed above are linearly independent or linearly dependent. If is …