Take the upper triangularize of a matrix

Questions
1

Hi,

I have a matrix like this
mtr = {{a, b, c, d}, {x, y, z, c}, {1, 2, 3, 4}, {3, 6, 8, 9}};

I applied this operation

cc = UpperTriangularize[mtr]

so I have .

cc = {{a, b, c, d}, {0, y, z, c}, {0, 0, 3, 4}, {0, 0, 0, 9}}

Now I would create a vector with only the values different to zero. How do I do?
Hence I would obtain the follow resut:
cc = {a,b,c,d,y,z,c,3,4,9}

Thanks for your help.

Margherita

2

Hi,

this could work:

DeleteCases[Flatten[cc], 0]

Cheers,

Marco

3

Thank you!

4

Start with the upper triangular matrix.

cc = {{a, b, c, d}, {0, y, z, c}, {0, 0, 3, 4}, {0, 0, 0, 9}};

If you want to remove the lower part but keep zeros, if any, that occur in the upper part, you can just extract the appropriate diagonals.

Flatten[Map[Diagonal[cc, #] &, Range[0, Length[cc] - 1]]]

(* Out[60]= {a, y, 3, 9, b, z, 4, c, c, d} *)

If you want to remove all zeros, there is the method shown by @Marco Thiel. An alternative is to convert to an explicit SparseArray and extract all but the default value, as below.

Most[ArrayRules[SparseArray[cc]][[All, 2]]]

(* Out[66]= {a, b, c, d, y, z, c, 3, 4, 9} *)
5

Thanks, a lot but …Another help please,
if I have
cc = {{{a, b, c, d}, {0, y, z, c}}, {{0, 0, 3, 4}, {0, 0, 0, 9}}};
Which are the best commands to create this :

cc ={ {a, b, c, d, y, z, c}, {3, 4, 9} }

Delete th zero values and to maintain the same level.

Best regards.

Margherita

6

Hi,

this works:

Flatten[DeleteCases[#, 0, Infinity]] & /@ cc

Cheers,

Marco

7

thank you a lot!