3 deleted 242 characters in body
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Julia 0.6, 1013 bytes

So readable, and fairly short. max. applies the max function element wise to it's arguments. a' is the transpose of a. Normally I would define a function as f(a)=max.(a,a')max but after perusing other answers it seems common to use the header and footer in TIOelementwise to avoid function definition overheadit's arugments.

maxa->max.(a,a')

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Julia 0.6, 10 bytes

So readable, and fairly short. max. applies the max function element wise to it's arguments. a' is the transpose of a. Normally I would define a function as f(a)=max.(a,a') but after perusing other answers it seems common to use the header and footer in TIO to avoid function definition overhead.

max.(a,a')

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Julia 0.6, 13 bytes

max. applies the function max elementwise to it's arugments.

a->max.(a,a')

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2 avoid function definition overhead
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Julia 0.6, 1510 bytes

So readable, and fairly short. max. applies the max function element wise to it's arguments. a' is the transpose of a'. Normally I would define a function as f(a)==max.(a,a') is required to define a function, which is neccesary to allow mebut after perusing other answers it seems common to outputuse the answerheader and footer in the TIO footerto avoid function definition overhead. 

  
f(a)=maxmax.(a,a')

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Julia 0.6, 15 bytes

So readable, and fairly short. max. applies the max function element wise to it's arguments. a' is the transpose of a'. f(a)= is required to define a function, which is neccesary to allow me to output the answer in the TIO footer.

 
f(a)=max.(a,a')

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Julia 0.6, 10 bytes

So readable, and fairly short. max. applies the max function element wise to it's arguments. a' is the transpose of a. Normally I would define a function as f(a)=max.(a,a') but after perusing other answers it seems common to use the header and footer in TIO to avoid function definition overhead. 

 
max.(a,a')

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1
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Julia 0.6, 15 bytes

So readable, and fairly short. max. applies the max function element wise to it's arguments. a' is the transpose of a'. f(a)= is required to define a function, which is neccesary to allow me to output the answer in the TIO footer.

f(a)=max.(a,a')

Try it online!