# To find the maximum value in a matrix?

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Sabarinathan Vadivelu
on 5 Sep 2012

Commented: Steven Lord
on 11 Dec 2022

Let me have a 3X3 matrix

6 8 9

7 10 11

21 22 8

How to find the maximum value from this matrix?

##### 2 Comments

KHOIROM Motilal
on 17 Mar 2016

Edited: KHOIROM Motilal
on 17 Mar 2016

- clc
- close all
- clear all
- X=[99 67 65;
- 63 62 61;
- 41 40 9];
- MAX=X(1,1);
- for i=1:3
- for j=1:3
- if MAX<= X(i,j);
- MAX=X(i,j);
- end
- end
- end
- disp(MAX)

### Accepted Answer

Michael Völker
on 5 Sep 2012

Edited: Steven Lord
on 25 Mar 2020

Starting in R2018b, you can use the following command to find the maximum over all elements in an array A:

M = max(A, [], 'all');

For previous releases, use:

M = max(A(:));

##### 4 Comments

Stephen23
on 11 Dec 2022

"what do the empty square brackets represent?"

Steven Lord
on 11 Dec 2022

The max function's first two inputs are the two matrices whose values you want to compare. If you only want to compute the maximum of one matrix, you need something to use as a placeholder for that second matrix. Otherwise if you wrote something like this, are you asking for the maximum of the elements of a matrix and the value 1 or are you asking for the maximum along the 1st dimension?

max(A, 1)

To break that ambiguity, that syntax is interpreted as the former (the maximum of the elements of A and the value 1) while the following is the latter (the maximum along the 1st dimension.)

max(A, [], 1)

### More Answers (5)

Azzi Abdelmalek
on 5 Sep 2012

max(max(A))

##### 4 Comments

Jonathan Posada
on 20 Feb 2016

DGM
on 11 Dec 2022

Not that this is a good idea, but for an arbitrary number of dimensions:

A = rand(100,100,100,10); % a fairly large ND array

% find global maximum of A

maxval = max(A);

for n = 2:ndims(A)

maxval = max(maxval);

end

maxval

It hasn't been so for quite some time, but in my experience, this iterative approach had a significant speed advantage with larger N-D arrays in older versions (2x-3x as fast as max(A(:)) for the arrays I was using). I don't remember if that advantage still existed in R2012x, but it did in R2009b. In current versions, using vectorization or 'all' are faster for small arrays and roughly equivalent for large arrays. That's on my hardware, so I make no guarantees that it's exactly universal.

Performance aside, it's hard to justify this verbose method over the canonical techniques, if only for the sake of readability.

It's not something I'd recommend, and I doubt that the legacy performance is the typical reason that people gravitate to the approach, but I thought it was interesting to note for old time's sake.

Tom
on 28 Jan 2020

##### 2 Comments

John Doe
on 31 Jan 2020

This should be upvoted and/or somehow appear closer to the chosen answer, as M = max(A,'all') seems not to work at all in R2018b+ (returning the entire matrix).

M = max(A(:)) seems to work in R2018b+ and presumably universally.

Steven Lord
on 25 Mar 2020

The [] as the second input is required when you want to specify a dimension, including 'all'. The function call max(A, 'all') only works if A and 'all' are compatibly sized.

>> max(1:3, 'all')

ans =

97 108 108

>> max(1:3, [], 'all')

ans =

3

Dmaldo01
on 22 Apr 2016

Edited: Dmaldo01
on 22 Apr 2016

This will work for all dimensions. If more efficient than ind2sub for less than 16000 elements.

[M,Index] = maxEl(MatVar)

index = size(MatVar);

Index = index*0;

M = max(MatVar(:));

A = find(MatVar==max(MatVar(:)),1);

for i = 1:length(index)

Index(i) = mod(ceil(A),index(i));

A = A/index(i);

end

Index(Index==0)=index(Index==0);

##### 0 Comments

Yokesh
on 16 May 2019

If matrix dimension is 'n', then max element can be found by:

max(max(.....maxn^2((A))...)

We have to include n^2 times max

##### 2 Comments

Steven Lord
on 16 May 2019

JPS
on 6 Feb 2021

or you can use,

M = max(max(A));

##### 2 Comments

Adrian Brown
on 15 Mar 2021

hello,

There is any way for a matrix size NxM to get the k maximum element in the whole matrix not in rows or colomns but in only elements. for example matrix A = [1 3 2 5, 7 9 12 8, 12 8 9 0] for K= 3 the 3 maximum elements are 12 9 and 8 and I want to return there location in the matrix.

I really appreciate any help

Walter Roberson
on 15 Mar 2021

A = [1 3 2 5; 7 9 12 8; 12 8 9 0]

[best3, best3idx] = maxk(A(:),3)

The three maximum values are 12, 12, and 9, not 12, 9, and 8. If you are interested in the three maximum unique values, then you need to explicitly take into account that some values occur more than once.

k = 3;

uA = unique(A, 'sorted');

nresults = min(length(uA), k);

results = cell(nresults, 1);

for K = 1 : k

this_max = uA(end-K+1);

results{K,1} = this_max;

results{K,2} = find(A==this_max).';

end

disp(results)

The output is a cell array, in which the first column gives you the value that is the maximum, and the second column gives you all the linear indices into the array. The code could be modified to give row and column outputs instead without much change.

The code does not assume that the number of occurrences is the same for each of the values (if that were known to be true then a numeric array could be created instead of a cell array.)

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