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What is the geometric interpretation of a matrix with only one element? If it means One dimension then how to identify the dimension viz X,YorZ?

Mahesh
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2 Answers2

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This is not an answer just a share of thought or discussion.

In general,the concept of matrix is related to linear transformations from some dimensional space to some dimensional space and in case of a $1 \times 1$ matrix, we must have a linear transformation from a One-dimensional space to one-dimensional space. The way you want the dimension i.e. X,Y or Z is not defined in 1-D space. It has only one dimension.

Sujit Bhattacharyya
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  • Thanks for replying...My Query is if we can represent the 22 matrix using column vectors. How are we going to represent 11 matrix geometrically? – Mahesh Aug 19 '18 at 07:02
  • did you mean this: Let, $A_{1\times 1}=(a){1\times 1}$ then $A{1\times 1}=a\bullet (1)_{1\times 1}$, $a$ is a scalar quantity. – Sujit Bhattacharyya Aug 20 '18 at 09:59
  • Actually I got to know that the numbers used in the matrix are actually the multiple of unit vectors that shows that a 1*1 matrix is a vector and not a scalar. – Mahesh Aug 21 '18 at 11:08
  • check this out : https://www.quora.com/Is-a-1-x-1-matrix-a-scalar – Sujit Bhattacharyya Aug 22 '18 at 03:58
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A $1 \times 1$ matrix is a number. To represent a number, all you need is a number line. If you prefer, you can think of this number line as an "$x$-axis".

If you represent a $2 \times 2$ matrix with $2$-dimensional "column vectors", then the analogous representation of a $1 \times 1$ matrix would be an arrow on the number line, pointing from zero. That is, we can represent numbers as vectors on our $x$-axis.

Ben Grossmann
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