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Jul
27
comment The difference between vector space and group
@BrianFitzpatrick That's what I need. I just wondering if I can define a basis in the $\mathbb{Z}$ module. For example let $x^2=x\cdot x$,$x^{-1}$ as the inverse element of $x$,$x^{-2}=x^{-1}\cdot x^{-1}$
Jul
27
accepted SOR method converges for $\left( \begin{array}{ccc}2& -1\\-2 & 2\end{array} \right)$
Jul
27
accepted Prove the matrix $\left( \begin{array}{ccc}A_{11}&A_{12}\\A_{21}&B_{22}+A_{21}A_{11}^{-1}A_{12}\end{array}\right)$ spd
Jul
27
accepted Euclidean space and Euclidean geometry
Jul
27
accepted Does every inner product space has an orthogonal basis?
Jul
27
asked The difference between vector space and group
Jul
23
comment Does every inner product space has an orthogonal basis?
But I think it is a basis
Jul
23
comment Does every inner product space has an orthogonal basis?
I can't see why it is not in the span?
Jul
23
comment Does every inner product space has an orthogonal basis?
@deftfyodor no,it is just for finite case
Jul
23
asked Does every inner product space has an orthogonal basis?
Jul
23
accepted Space that can not define an inner product
Jul
22
comment Space that can not define an inner product
If u arrange the set well-ordered, how can u get an upper bound for each subset?
Jul
22
comment Space that can not define an inner product
I can't see how u use axiom of choice to choose a basis. From the axiom of choice,we can form a set of elements which we choose one from each subset, then how can we choose the basis?
Jul
22
asked Space that can not define an inner product
Jul
22
asked Geometric interpretation of parallelogram law determines the inner product
Jul
22
comment Euclidean space and Euclidean geometry
@B.S. differential geometry maybe more likely.
Jul
22
asked Euclidean space and Euclidean geometry
Jul
22
asked The inner product determines the structure of the space
Jul
20
accepted The rule of operator “+”
Jul
16
accepted Why group needs zero and negative number