- How to prove $ (AB)^T=B^T A^T$ - Mathematics Stack Exchange
Given an $m\times n$ -matrix $A$ and an $n\times p$ -matrix $B$ Prove that $ (AB)^T = B^TA^T$
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EZEKIEL4 SANDERS (ANDREW JACKSON3, GEORGE W 2, ISAAC1) was born Abt 1857 in Louisville, Winston County, Mississippi, USA He married LOUISA LUCY M EVANS 26 Dec 1877 in Winston County, Mississippi, USA
- How to prove that $(AB)^t = B^tA^t$ - Mathematics Stack Exchange
The proof given in my book (and I came up with as well) is: However, the part that throws me off is line #3 where they do $\\Sigma A_{jk} B_{ki} = \\Sigma B_{ki} A_{jk}$ I understand that multiplica
- Stuck on proving $(AB)^t=B^tA^t$ - Mathematics Stack Exchange
Let A ∈ Mm,n(C), B ∈Mn,p(C) A ∈ M m, n (C), B ∈ M n, p (C) I need to show that (AB)t = BtAt (A B) t = B t A t I know that this is a very well-known property, but I am a bit stuck So, I considered that A = (aij)1≤i≤m 1≤j≤n A = (a i j) 1 ≤ i ≤ m 1 ≤ j ≤ n and B = (bjk)1≤j≤n 1≤k≤p B = (b j k) 1 ≤ j ≤ n 1 ≤ k ≤ p and then I took X = AB = (xik)1≤i≤m 1
- $AB=BA$ implies $AB^T=B^TA$ when $A$ is normal
AB = BA A B = B A implies ABT = BTA A B T = B T A when A A is normal Ask Question Asked 11 years, 4 months ago Modified 5 years, 5 months ago
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She married William MCCURRY , Sr ABT 1788 in North Carolina He was born BET 1763 - 1765 in Augusta, Virginia or Lincoln or Rutherford Co North Carolina, and died 11 OCT 1828 in Golden Valley, Rutherford Co , N C
- linear algebra - Proof that $ (A^t)^t=A$, $ (A+B)^t=A^t+B^t$, $ (AB)^t . . .
In a linear algebra textbook, I was given the following problem: If B B is a n × n n × n square matrix, show that BBt B B t is symmetric and B −Bt B − B t is skew-symmetric
- Proof that $(A+B)^T=A^T+B^T$ (homework question)
Homework question: Proof that (A + B)T =AT +BT (A + B) T = A T + B T Let A and B be m × n m × n matrices Prove that (A + B)T =AT +BT (A + B) T = A T + B T by comparing the ij-th entries of the matrices on each side of this equation (Let A = (aij) A = (a i j) and B = (bij B = (b i j) ) I am not sure how to do this proof, I know how to prove it by substituting ij-th entries with arbitrary
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