﻿ Matrices operations calculator
Operations on two matrices
 Matrix   A
 Scalar multiply:
 Determinant: Rank: Trace:
 Matrix   B
 Scalar multiply:
 Determinant: Rank: Trace:
 Result Matrix   C
 Scalar multiply:
 Determinant: Rank: Trace:
 Determinants Eigenvalues Inverse Overview Rank Rotation Scaling Transposed Types NOTES
 Matrices Types ▲ Matrices overview ▲
The notation of a matrix of size (m n) is defined as     A(m n) = A(row, column)
A convenient shorthand which offers considerable advantage when working with system of linear equations is by using the matrix notation. Consider the set of linear equations of the form: In matrix notation these equations may be represented as: or     AX = C
 The terms of the matrix can be represented as: Distributive law
Left side      A(B + C) = AB + AC

Right side    (A + B)C = AC + BC
A(m n)     B and C (n p)

A and B (m n)     C(n p)
Associative law
Addition    (A + B) + C = A + (B + C)

Multiplication        (AB)C = A(BC)
(m n)

(n n)
Scalar multiplication (kA)B = A(kB) = k(AB) A(m n)      B(n p)
k any number
Commutative law
Addition       A + B = B + A

Multiplication        not commutative
A and B (m n)

Because    A∙B ≠ B∙A
Other algebric laws

(k, v are constants)
 0 + A = A k(A + B)= kA + kB 1 · A = A (k + v)A = kA + vA 0 · A = 0 k(vA) = (kv)A A + ( A) = 0 kA = 0    →    k = 0   or   A = 0 (  1)A =  A
Matrices powers

(c is constant)  Matrices addition and multiplication ▲
Matrices addition:
A and B are of the same size    m × n Scalar multiplication Matrices multiplication     A (m × n) ∙ B (n × p) = C (m × p) Example:  