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Introduction to Matrices

Matrix identifier. Enter a matrix to detect its dimensions and type—square, diagonal, symmetric, triangular—with notes.

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A = (aᵢⱼ)ₘ×ₙ
space-separated entries, semicolon-separated rows, e.g. 1 2;3 4

📖 Tutorial｜Introduction to Matrices

1. Definition
A rectangular array of m×n numbers in m rows and n columns is a matrix, A=(aᵢⱼ)ₘ×ₙ. When m=n it is an n×n square matrix.
2. Symbols
SymbolMeaning
aᵢⱼentry in row i, column j
m, nrows and columns
Iidentity matrix (diagonal entries 1)
Ozero matrix (all entries 0)
3. How this tool works
  • Rows are separated by semicolons, columns by spaces;
  • Rows = number of semicolon blocks; columns = entries per row;
  • m=n means a square matrix;
  • Off-diagonal zeros give a diagonal matrix; diagonal ones give the identity.
4. Steps
  1. Type the matrix text;
  2. Click Calculate to see dimensions and type;
  3. Use Load Example to try the identity.
5. Example
Example: Enter 1 0;0 1. It is a 2×2 square matrix, off-diagonal zeros make it diagonal, and diagonal ones make it the identity I.
6. Pitfalls
Every row must have the same number of entries;
Square only requires m=n, not diagonal entries;
A zero matrix means all entries are 0, not determinant 0.

❓ FAQ｜Introduction to Matrices

Matrix vs determinant?
A matrix is an array of numbers; a determinant is a single number and only defined for square matrices.
What is a square matrix?
One with equal rows and columns, e.g. 2×2 or 3×3.
What is the identity matrix for?
It acts like 1 in multiplication: AI=IA=A.
Diagonal vs identity?
The identity is a special diagonal matrix with all diagonal entries equal to 1.
What input format?
Semicolons separate rows, spaces or commas separate columns, e.g. 1 2;3 4.