Matlab<DELIMITER/>Mathematica<DELIMITER/>remarks

"In Matlab, everything is a matrix."<DELIMITER/>"In Mathematica, everything is an expression."<DELIMITER/>

`[]`<DELIMITER/>`{}`<DELIMITER/>empty list

`[1 2 3]`<DELIMITER/>`{1, 2, 3}`<DELIMITER/>

`[1; 2; 3]`<DELIMITER/>`{{1}, {2}, {3}}`<DELIMITER/>

`[1 2; 3 4]`<DELIMITER/>`{{1, 2}, {3, 4}}`<DELIMITER/>

`% this is a comment`<DELIMITER/>`(* this is a comment *)`<DELIMITER/>

`command1; command2;`<DELIMITER/>`command1; command2;`<DELIMITER/>In both Mathematica and Matlab, `;` indicates the end of a command and suppresses its output.

`command1, command2`<DELIMITER/>`command1; command2`<DELIMITER/>Matlab commands can be chained by `,`; Mathematica commands can't be chained by `,`.

`'Hello world!'`<DELIMITER/>`"Hello world!"`<DELIMITER/>Matlab uses single quote for string. Mathematica uses double.

`% this is a comment`<DELIMITER/>`(* this is a comment *)`<DELIMITER/>

`command1; command2;`<DELIMITER/>`command1; command2;`<DELIMITER/>In both Mathematica and Matlab, `;` indicates the end of a command and suppresses its output.

`command1, command2`<DELIMITER/>`command1; command2`<DELIMITER/>Matlab commands can be chained by `,`; Mathematica commands can't be chained by `,`.

`'Hello world!'`<DELIMITER/>`"Hello world!"`<DELIMITER/>Matlab uses single quote for string. Mathematica uses double.

`5:2:25` or `[5:2:25]`<DELIMITER/>`Range[5, 25, 2]`<DELIMITER/>

`x(2:4)`<DELIMITER/>`x\\[[2;;4]]`<DELIMITER/>

`x(2, 3)`<DELIMITER/>`x\\[[2, 3]]`<DELIMITER/>

`x(:, 2)`<DELIMITER/>`x\\[[All, 2]]`<DELIMITER/>

`x(2, :)`<DELIMITER/>`x\\[[2, All]]`<DELIMITER/>

`x([1 3], :)`<DELIMITER/>`x\\[[{1, 3}, All]]`<DELIMITER/>

`x(1:3, :)`<DELIMITER/>`x\\[[1;;3, All]]`<DELIMITER/>

`x([1 3], [2 3])`<DELIMITER/>`x\\[[{1, 3}, {2, 3}]]`<DELIMITER/>

`x(:, 2) = [1; 2; 3]`<DELIMITER/>`x = Join[x\\[[{1}]], Transpose[{1, 2, 3}], x\\[[All, 3;;]], 2]`<DELIMITER/>Mathematica needs `x = ` explicitly to get `x` updated

`x(:)`<DELIMITER/>`Flatten[Transpose[x]]`<DELIMITER/>Concatenate columns to one column.

`y=x'`, `y(:)'`<DELIMITER/>`Flatten[x]`<DELIMITER/>Concatenate rows to one row.

`m=[1, 2; 3, 4; 1, 1]; size(m)`<DELIMITER/>`m={{1, 2}, {3, 4}, {1, 1}}; Dimensions[m]`<DELIMITER/>matrix dimension

`[x [3; 5; 2]]`<DELIMITER/>`Join[x, Transpose[{3, 5, 2}], 2]`<DELIMITER/>Append a column to a matrix, assuming there are 3 rows.

`[x' [1; 6]'`<DELIMITER/>`Append[x, {1, 6}]`<DELIMITER/>Append a row to a matrix, assuming there are 2 columns

`[x y]`<DELIMITER/>`Join[x, y, 2]`<DELIMITER/>Horizontally concatenate two matrices, assuming `size(x, 1)` equals `size(y, 1)` and `Dimensions[x, 1]` equals `Dimensions[y, 1]`

`m1*m2`<DELIMITER/>`m1.m2`<DELIMITER/>Matrix multiplication, assuming `m1` is `n × m` matrix and `m2` is `m × p` matrix.

`m1 .* m2`<DELIMITER/>`MapThread[Times, {m1, m2}]`<DELIMITER/>Elementwise matrix multiplication, assuming `m1` and `m2` are `n × m` arrays.

`m .^ 2`<DELIMITER/>`Map[#^2&, m, {2}]`<DELIMITER/>Elementwise exponentiation. Notice by virtue of Listability attribute of `Power`, `Map[#^2&, m]` which is equivalent to `Map[#^2&, m, 1]` also works.

`exp(m)`<DELIMITER/>`Exp[m]` or `E^m`<DELIMITER/>Elementwise exponentiation.

`log(m)`<DELIMITER/>`Log[m]`<DELIMITER/>Elementwise logrithm.

`abs(m)`<DELIMITER/>`Abs[m]`<DELIMITER/>Elementwise absolute value.

`-m`<DELIMITER/>`-m`<DELIMITER/>Elementwise negation.

`ones(3, 4)`<DELIMITER/>`Table[1, {3}, {4}]`<DELIMITER/>Matrix of ones.

`m + 1`<DELIMITER/>`m + 1`<DELIMITER/>Elementwise addition. `m` is a matrix.

`m'`<DELIMITER/>`Transpose[m]`<DELIMITER/>Matrix transpose.

`pinv(m)`<DELIMITER/>`Inverse[m]`<DELIMITER/>Matrix inverse.

`sum(m)`<DELIMITER/>`Total[Transpose[matrix], {2}]`<DELIMITER/>Columnwise sum.

`sum(m,1)`<DELIMITER/>`Total[Transpose[matrix], {2}]`<DELIMITER/>Columnwise sum.

`sum(m,2)`<DELIMITER/>`List/@Total[matrix, {2}]`<DELIMITER/>Row-wise sum.

`prod(m)`<DELIMITER/>`Apply[Times, m]` or `Times@@m`<DELIMITER/>Columnwise product. `Times[{1, 3}, {2, 4}]` has threading behavior.

`floor(m)`<DELIMITER/>`Floor[m]`<DELIMITER/>Elementwise flooring.

`ceil(m)`<DELIMITER/>`Ceiling[m]`<DELIMITER/>Elementwise ceiling.

`max(m)`<DELIMITER/>`Max /@ Transpose[m]`<DELIMITER/>Columnwise maximum.

`max(m1, m2)` <DELIMITER/>`Table[Max[m1\\[[i, j]], m2\\[[i, j]]], {i, Length[m1]}, {j, Length[Transpose[m1]]}]`<DELIMITER/>Elementwise maximum.

`max(magic3, [], 1)`<DELIMITER/>`Max /@ Transpose[magic3]`<DELIMITER/>Columnwise maximum.

`max(magic3, [], 2)`<DELIMITER/>`{Max[#]} & /@ magic3`<DELIMITER/>Row-wise maximum.

`max(max(magic3))` or `max(magic3(:))`<DELIMITER/>`Max[magic3]`<DELIMITER/>Maximum matrix element.

`[maxval idx] = max(m)`<DELIMITER/>`maxval = Max /@ Transpose[m]; idx = MapThread[Position[##]\\[[1,1]]&, {Transpose[m], Max /@ Transpose[m]}]`<DELIMITER/>

`m < 2`<DELIMITER/>`Map[#<2&, m, {2}]`<DELIMITER/>Elementwise test. Notice `{2}` isn't neglegible as `Less` isn't Listable (`Attributes[Less]` doesn't contain `Listable`).

`magic(3)`<DELIMITER/><DELIMITER/>[A Mathematica program for constructing odd-order magic squares](http://demonstrations.wolfram.com/MagicSquare/).

`flipud(magic3)`<DELIMITER/>?<DELIMITER/>Flip matrix up/down direction.

`fliplr(magic3)`<DELIMITER/>?<DELIMITER/>Flip matrix left/right direction.

`magic3 = magic(3)`, `find(m<5)`<DELIMITER/>`Select[Flatten[Transpose[magic3]], #<5&]`<DELIMITER/>Find positions of elements less than 3.

`[r,c] = find(magic3<5)`<DELIMITER/>`{r, c} = {#\\[[All, 1, 1]], #\\[[All, 1, 2]]} &[Position[magic3, #] & /@ Cases[magic3, _?(# > 5 &), {2}]]`<DELIMITER/>Why the ordering of results are different?

`eye(3)`<DELIMITER/>`IdentityMatrix[3]`<DELIMITER/>Identity matrix.

`rand()`<DELIMITER/>`RandomReal[]`<DELIMITER/>or `rand`

`rand(3)`<DELIMITER/>`Table[RandomReal[], {3}, {3}]`<DELIMITER/>Create matrix with random reals.

`x = rand(2, 3)`<DELIMITER/>`x = RandomReal[{0, 1}, {2, 3}]`<DELIMITER/>

`disp(m)` or `disp('hello')`<DELIMITER/>`Print[m]` or `Print["Hello"]`<DELIMITER/>

`who`<DELIMITER/>`Names["*"]`<DELIMITER/>

`whos`<DELIMITER/><DELIMITER/>?

`clear`<DELIMITER/>`Clear[]`<DELIMITER/>

`clear('x')`<DELIMITER/>`Clear[x]`<DELIMITER/>

`load('file.dat')`<DELIMITER/>`Import["file.dat","Data"]`<DELIMITER/>`file.dat` contains tabulated numbers

`save file.mat x`<DELIMITER/>`DumpSave["file.mx", x]`<DELIMITER/>

`save file.txt x --ascii`<DELIMITER/>`Export["file.txt", "Data"]`<DELIMITER/>

`save file.mat x`<DELIMITER/>`DumpSave["file.mx", x]`<DELIMITER/>

`matlab -nodesktop`<DELIMITER/>`math` (Linux), `MathematicaKernel` (Mac OS X, Windows), or `MathematicaScript -script`<DELIMITER/>Non-GUI session.

<DELIMITER/>`MathematicaScript -script`<DELIMITER/>Scripting.

`magic(3)`<DELIMITER/><DELIMITER/>[A Mathematica program for constructing odd-order magic squares](http://demonstrations.wolfram.com/MagicSquare/).

`flipud(magic3)`<DELIMITER/>?<DELIMITER/>Flip matrix up/down direction.

`fliplr(magic3)`<DELIMITER/>?<DELIMITER/>Flip matrix left/right direction.

`magic3 = magic(3)`, `find(m<5)`<DELIMITER/>`Select[Flatten[Transpose[magic3]], #<5&]`<DELIMITER/>Find positions of elements less than 3.

`[r,c] = find(magic3<5)`<DELIMITER/>`{r, c} = {#\\[[All, 1, 1]], #\\[[All, 1, 2]]} &[Position[magic3, #] & /@ Cases[magic3, _?(# > 5 &), {2}]]`<DELIMITER/>Why the ordering of results are different?

`eye(3)`<DELIMITER/>`IdentityMatrix[3]`<DELIMITER/>Identity matrix.

`rand()`<DELIMITER/>`RandomReal[]`<DELIMITER/>or `rand`

`rand(3)`<DELIMITER/>`Table[RandomReal[], {3}, {3}]`<DELIMITER/>Create matrix with random reals.

`x = rand(2, 3)`<DELIMITER/>`x = RandomReal[{0, 1}, {2, 3}]`<DELIMITER/>

`disp(m)`<DELIMITER/>`Print[m]`<DELIMITER/>`m` is a matrix/expression.

`fprintf('hello world!\n')`<DELIMITER/>Print["Hello world!"]`<DELIMITER/>

`find(m > 1)`<DELIMITER/>`Positions[m, _?(#>1&)]`<DELIMITER/>find indices of elements of matrix `m` that is larger than 1

`pack`<DELIMITER/>`Share[]`<DELIMITER/>Consolidate memory.

`who`<DELIMITER/>`Names["*"]`<DELIMITER/>

`whos`<DELIMITER/><DELIMITER/>?

`clear`<DELIMITER/>`Clear[]`<DELIMITER/>

`clear('x')`<DELIMITER/>`Clear[x]`<DELIMITER/>

`load('file.dat')`<DELIMITER/>`Import["file.dat","Data"]`<DELIMITER/>`file.dat` contains tabulated numbers

`save file.mat x`<DELIMITER/>`DumpSave["file.mx", x]`<DELIMITER/>

`save file.txt x --ascii`<DELIMITER/>`Export["file.txt", "Data"]`<DELIMITER/>

`save file.mat x`<DELIMITER/>`DumpSave["file.mx", x]`<DELIMITER/>

`matlab -nodesktop`<DELIMITER/>`math` (Linux) `MathematicaKernel` (Mac OS X, Windows), or `MathematicaScript -script`<DELIMITER/>Non-GUI session.