Recent content by vdgreat

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    Undergrad What is the proof for the similarity of two matrices having the same rank?

    can anyone help me with this proof rank of two similar matrices is same.
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    Graduate Is the Intersection of Even and Odd Function Subspaces Only the Zero Function?

    do we need contradiction? and how about c) any idea??
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    Graduate Is the Intersection of Even and Odd Function Subspaces Only the Zero Function?

    for b) i said E\capO= {f\epsilonv | f(x)= f(-x) and f(x)=-f(-x), \forallx\epsilonR} E\capO= {f\epsilonv | f(x)= -f(x), \forallx\epsilonR} E\capO= {f\epsilonv | f(x)= 0, \forallx\epsilonR} E\capO= {0} (f(x) =0 is the zero function) what do you think?
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    Graduate Is the Intersection of Even and Odd Function Subspaces Only the Zero Function?

    i did a) trying b and see where it leads thanks
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    Graduate Is the Intersection of Even and Odd Function Subspaces Only the Zero Function?

    Let V be the vector space of all functions from R to R, equipped with the usual operations of function addition and scalar multiplication. Let E be the subset of even functions, so E = {f \epsilon V |f(x) = f(−x), \forallx \epsilon R} , and let O be the subset of odd functions, so that O = {f...
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    Undergrad Prove Commutation Property for 2x2 Matrices D

    i got it thanks
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    Graduate How Can You Prove the Commutative Property of Vector Addition in Rn Spaces?

    let u={u1, u2...,un) v={v1,v2...,vn) then u+v= {u1+v1, u2+v2,...,un+vn} (vector addition) or, u+v= {v1+v1, v2+u2,...,vn+un} (commutative property of addition on R) therefore, u+v=v+u (vector addition)
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    Undergrad Prove Commutation Property for 2x2 Matrices D

    for each of the above matrices, i found out that it is true. but how can i prove this without having knowledge of basis. i haven't don't it yet.
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    Undergrad Prove Commutation Property for 2x2 Matrices D

    help with this problem anyone?
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    Undergrad Prove Commutation Property for 2x2 Matrices D

    but how can i prove it or generalize it??
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    Undergrad Prove Commutation Property for 2x2 Matrices D

    Let D = [d11 d12] [d21 d22] be a 2x2 matrix. Prove that D commutes with all other 2x2 matrices if and only if d12 = d21 = 0 and d11 = d22. I know if we can prove for every A, AD=DA should be true, but I really don't know how to proceed from there. I tried equating elements of AD with...