If I have a 4x4 cell array, 'm' where each element is a matrix expressed as '4x4 double', what would be the notation to access the values of a matrix within 'm'.

    say m = 4x4 double 4x4 double 4x4 double 4x4 double
            4x4 double 4x4 double 4x4 double 4x4 double
            4x4 double 4x4 double 4x4 double 4x4 double
            4x4 double 4x4 double 4x4 double 4x4 double

each 4x4 when opened is a matrix. say the matrix '4x4 double' in row one column one of 'm', has a value of one in it's first row and first column so [1,1]=1 of the first row first column of matrix 'm' . how could i access that without assigning each 4x4 double its own variable. for instance, could i do 1=m{1,[1,1], 1}?

[Stephen23]

@Andrew Wiebe: I changed your title to use the correct terminology "cell array", because using the term "matrix" is completely ambiguous: the term "matrix" is often understood to refer to numeric arrays. It is worth learning to use the correct terminology, as this helps us communicate better.

[James Tursa]

"...the term "matrix" is often understood to refer to numeric arrays."

Is this documented somewhere? I had never heard that before, and not sure I even agree with it. I have always understood the term "matrix" in MATLAB to be a 2D object ... any object. E.g., read the doc for transpose and it talks about operations on a "matrix". The doc states that this works for numeric, char, logical, cell, struct, class objects, etc. Clearly the term matrix is used in a generic 2D sense here. Other places in the doc sometimes refer to both "matrices" and "cell arrays" in the same sentence, so the doc isn't even consistent here.

I would have said if one wants to be specific about numeric 2D objects then one can use the term "numeric matrix".

[Stephen23]

https://en.wikipedia.org/wiki/Matrix_(mathematics): "In mathematics, a matrix (plural matrices) is a rectangular array[1]—of numbers, symbols, or expressions, arranged in rows and columns" (the entirety of this page explains properties of numeric matrix manipulation).

http://mathworld.wolfram.com/Matrix.html: "A matrix is a concise and useful way of uniquely representing and working with linear transformations..." (i.e. numeric values and their abstractions)

http://dictionary.reference.com/browse/matrix: " 11. Mathematics. a rectangular array of numbers, algebraic symbols, or mathematical functions, especially when such arrays are added and multiplied according to certain rules. " (clearly numeric and their abstractions)

http://www.mathsisfun.com/algebra/matrix-introduction.html: "A Matrix is an array of numbers"

http://www.oxforddictionaries.com/definition/english/matrix: "4 Mathematics A rectangular array of quantities or expressions in rows and columns that is treated as a single entity and manipulated according to particular rules:" (i.e. numeric values and their abstractions)

That the meaning of matrix has been applied to other data structures is hinted at by Merriam Webster:

http://www.merriam-webster.com/dictionary/matrix: "5 a : a rectangular array of mathematical elements (as the coefficients of simultaneous linear equations) that can be combined to form sums and products with similar arrays having an appropriate number of rows and columns b : something resembling a mathematical matrix especially in rectangular arrangement of elements into rows and columns "

I did not state that "matrix" does not also refer to cell arrays, structures and other data classes within MATLAB, I stated that "the term "matrix" is completely ambiguous", because, exactly as you point out, it can be applied in MATLAB to many different classes of data.

Answer 1

[James Tursa]

For a cell array m,

m(i,j) is the i'th row, j'th column element of m. m(i,j) is a 1x1 cell array.

m{i,j} is the _contents_ of the i'th row, j'th column element of m. In your case a 4x4 double.

m{i,j}(x,y) is the x'th row, y'th column element of the 4x4 double array in m{i,j}.  A 1x1 scalar double.

m{i,j}(x,y) = 6;  Sets the x'th row, y'th column element of the 4x4 double array in m{i,j} to 6.

v = m{i,j}(x,y);  Sets the variable v equal to the x'th row, y'th column element of the 4x4 double array in m{i,j}.

Answer 2

[Andrew Wiebe]

Wonderful! one other thing, I'm trying to set two separate variables in a for loop to be a range of numbers i.e. n=1:42 l=1:53. Whenever i run it though it always labels them as being one scalar number and i only get a small portion of my results. how can i set it so when it loops it doesnt stop?

[James Tursa]

You will need to show your code so we can see what you are doing and offer suggestions on how to correct things. If this is unrelated to the original cell array indexing question above, you should open up a new Question.