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 Oct20 asked Different results for row reduction in Matlab Oct19 accepted Showing that $\{ 1, \cos t, \cos^2 t, \dots, \cos^6 t \}$ is a linearly independent set Oct10 comment Showing that $\{ 1, \cos t, \cos^2 t, \dots, \cos^6 t \}$ is a linearly independent set Thank you for your answer, Arturo! I think my problem might stem from a misunderstanding of what linear independence requires. I thought for functions to be linearly independent, they need to be so for all $\mathbb{R}$; however, it seems like it's the other way around: i.e. if a set of functions are not linearly dependent for all $\mathbb{R}$, then they are linearly independent. So if we can show one example of linear independence, then we're done. Is that the gist of what you were saying? Oct10 comment Showing that $\{ 1, \cos t, \cos^2 t, \dots, \cos^6 t \}$ is a linearly independent set Thank you for your answer, André! Forgive me for asking, but it is not obvious to me why the fact that $\cos t$ can take on more than 6 different values makes a contradiction? Oct8 asked Showing that $\{ 1, \cos t, \cos^2 t, \dots, \cos^6 t \}$ is a linearly independent set Oct8 comment Showing that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set Thank you for the counterexample! Oct8 accepted Showing that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set Oct8 asked Showing that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set Sep18 awarded Enthusiast Sep4 comment Showing that $\mathbf{u}=\mathbf{0}$ for $c\mathbf{u}=\mathbf{0}$, $c$ nonzero Good point, thanks! Sep4 accepted Showing that $\mathbf{u}=\mathbf{0}$ for $c\mathbf{u}=\mathbf{0}$, $c$ nonzero Sep4 comment Showing that $\mathbf{u}=\mathbf{0}$ for $c\mathbf{u}=\mathbf{0}$, $c$ nonzero @Srivatsan: Good to know, thanks! Sep4 comment Showing that $\mathbf{u}=\mathbf{0}$ for $c\mathbf{u}=\mathbf{0}$, $c$ nonzero @Chandrasekhar: Thanks! Sep4 asked Showing that $\mathbf{u}=\mathbf{0}$ for $c\mathbf{u}=\mathbf{0}$, $c$ nonzero Sep3 revised Rotation of a vector distribution to align with a normal vector LaTeX for arctan, arccos. Sep3 suggested approved edit on Rotation of a vector distribution to align with a normal vector Sep1 comment editing signal in frequency domain and converting back to time domain You might want to post this at StackOverflow as well, for more answers (or even avp.stackexchange.com under signal-processing). Sep1 revised Is $\sin(x)/ \tan(x) = \cos(x)$ at $0$? Added LaTeX. Sep1 suggested approved edit on Is $\sin(x)/ \tan(x) = \cos(x)$ at $0$? Sep1 awarded Quorum