Special square matrices — A/L Combined Mathematics

What must I remember about Special square matrices?

• Square Matrix: A matrix with equal numbers of rows and columns (m = n, order n × n).
• Main (Principal) Diagonal: The diagonal entries a11, a22, ..., ann of a square matrix from top-left to bottom-right.
• Diagonal Matrix: A square matrix where all non-diagonal entries are zero (a_ij = 0 for all i ≠ j).
• Scalar Matrix: A diagonal matrix whose main diagonal entries are all equal (a_ii = k for all i).
• Identity (Unit) Matrix I: A scalar matrix whose main diagonal entries are all 1: A * I = I * A = A.

Test yourself (1 minute)

1. Trace of a matrix

   Sum of main diagonal elements: Tr(A) = a11 + a22 + ... + ann; Tr(AB) = Tr(BA).

2. Triangular matrices

   Upper Triangular matrix has all entries below main diagonal equal to zero (a_ij = 0 for i > j); Lower Triangular matrix has all entries above main diagonal zero.

3. Symmetric and Skew-Symmetric definitions

   A is Symmetric if A^T = A (a_ij = a_ji); A is Skew-Symmetric if A^T = -A (a_ij = -a_ji, implying all diagonal elements a_ii = 0).

Practise Special square matrices questions today

Source: NIE G.C.E. (A/L) Combined Mathematics Resource Book - Pure Mathematics, Unit 24

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Where does Special square matrices fit in the syllabus?

Year 2 · Term 1