Types of matrices: a galleryआव्यूहों के प्रकार: एक गैलरीMatrices ke types: ek gallery

NCERT 3.3 · Class 12 Maths · Chapter 3 · interactive diagram

Parts and what they mean

• Column matrix (स्तंभ आव्यूह) — Only one column: order m \times 1. Here 4 \times 1.
• Row matrix (पंक्ति आव्यूह) — Only one row: order 1 \times n. Here 1 \times 4.
• Square matrix (वर्ग आव्यूह) — Rows = columns (m = n). This one is a square matrix of order 3.
• Diagonal matrix (विकर्ण आव्यूह) — Square, and every element off the diagonal is 0 (b_{ij} = 0 for i \ne j).
• Scalar matrix (अदिश आव्यूह) — Diagonal matrix whose diagonal elements are all equal (here all 3).
• Identity matrix I_3 (तत्समक आव्यूह I_3) — Diagonal elements all 1, rest all 0. A scalar matrix with k = 1; IA = AI = A.
• Zero (null) matrix O (शून्य आव्यूह O) — All elements are zero. It need not be square; here 2 \times 3.
• Diagonal elements (विकर्ण के अवयव) — a_{11}, a_{22}, a_{33} — from top-left to bottom-right. Only square matrices have a diagonal.
• How the types nest (प्रकार एक-दूसरे में कैसे हैं) — Identity ⊂ scalar ⊂ diagonal ⊂ square: each inner type is a special case of the outer one.
• Square (वर्ग) — The biggest family: all n \times n matrices.
• Diagonal (विकर्ण) — Inside square: zeros off the diagonal.
• Scalar (अदिश) — Inside diagonal: equal diagonal entries k.
• Identity (तत्समक) — Inside scalar: k = 1.

Original diagram drawn by Simple Learning Hub, based on NCERT 3.3. Report a mistake