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If a subset of $S$, say $R$ is a basis for vector space $V$, then is $S$ also a basis for $V$?

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#linear-algebra #vector-spaces #change-of-basis
225
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Simultaneous triangularization of two matrices

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#linear-algebra #matrices #matrix-decomposition #change-of-basis #triangularization
42
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Orthogonal complement with non-standard dot product

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#orthogonality #change-of-basis
284
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Change of basis for functions in $\mathbb{C}$

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#linear-algebra #matrices #change-of-basis
92
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You are given $B,G,H,J$ bases for a real linear space $X$ and the change of basis transition matrices. What is the dimension of $X$?

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#linear-algebra #coordinate-systems #change-of-basis
58
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A vector $\mathbf{x}\in X$ has coordinates $\mathbf{x}_\mathcal{B}= \langle2,-7,-10\rangle$. What is $\mathbf{x}_\mathcal{G}$?

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#linear-algebra #coordinate-systems #change-of-basis #transition-matrix
304
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Computing the distance from a point and the plane?

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#linear-algebra #multivariable-calculus #affine-geometry #change-of-basis #projection-matrices
46
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Change of basis and independence problem

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#linear-algebra #change-of-basis
636
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Matrix exponential and change of basis

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#linear-algebra #trace #change-of-basis #matrix-exponential
268
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Why are the contravariant and covariant basis perpendicular?

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#tensors #change-of-basis
489
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Bijection from the set of all bases of the vector space $V$ (of dim $n$) to the set of all invertible matrices of order $n\times n$ such that:

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#linear-algebra #matrices #change-of-basis
153
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if $A$ is an $ n × n$ matrix, the A is the change of coordinates matrix from some bases $B$ and $C$ of $\mathbb R^n$

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#linear-algebra #matrices #change-of-basis
43
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How to calculate $f(p)_G$ where $p$ is given by$ p(x)=4 x^2+8 x+4 ∀x∈\Bbb R.$?

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#linear-algebra #coordinate-systems #change-of-basis
60
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Change of basis between $\mathbb{Q}(\sqrt{2}+ \sqrt{3})$ and $\mathbb{Q}(\sqrt{2}, \sqrt{3}) $

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#linear-algebra #abstract-algebra #change-of-basis
37
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Give the new basis $(H_k)_{k=0,1,2,3}$ Of $R_3[X]$ to express $P$ by $P(0),P(1),P'(0),P'(1)$

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#linear-algebra #polynomials #change-of-basis

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