Block-diagonal matrix from columns

MATL, 6 bytes

"@N$Yd

Works in current version (13.0.0) of the language/compiler.

Input has the following form, with semicolon as row separator, and commas or spaces as column separators within each row:

[1, 2, 3; 4, 5, 6]

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Explanation

"         % implicitly input 2D array and loop over its columns
  @       %   push column
  N$Yd    %   build block-diagonal matrix from all stack contents. Stack contents are
          %   a single column in the first iteration, or a partially built 2D array
          %   and a new column in all other iterations
          % end loop
          % implicit display

Worked example

Consider the input [1 2 3; 4 5 6]. The for loop beginning with " takes each column of the input. Within each iteration, @ pushes the current column onto the stack. So in the first iteration it pushes [1; 4]. N$ specifies that all the stack contents will be used as inputs of the following function, Yd.

This function (corresponding to MATLAB's blkdiag) "diagonally concatenates" its inputs to produce a block diagonal matrix (2D array). So in the first iteration Yd it takes one input and produces an output equal to that input, [1; 4], which is left on the stack.

In the second iteration the second column of the input, [2; 5], is pushed. Now Yd takes two 2×1 inputs, namely [1; 4] and [2; 5], and produces the 4×2 array [1 0; 4 0; 0 2; 0 5].

In the third iteration Yd takes the latter 4×2 array and the third column of the input, [3; 6], and produces the final result [1 0 0; 4 0 0; 0 2 0; 0 5 0; 0 0 3; 0 0 6].

ES6, 65 bytes

a=>[].concat(...a[0].map((_,i)=>a.map(b=>b.map((c,j)=>i-j?0:c))))

Takes as input and returns as output an array of arrays.

Mathematica, 40 39 Bytes

Credit to @Seeq for Infixing Flatten.

Transpose[DiagonalMatrix/@#]~Flatten~1&

Input is a list of row vectors delimited by {} brackets. So the initial example is represented by

{{1,2,3},{4,5,6}}

Generate an array of DiagonalMatrix where each one has diagonal elements from the rows of the input (3-D array). Transpose so the Flatten operation removes the correct bracket pairs to give the desired matrix (now 2-D array).