Mathematics reference
Rules for matrices
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Basic properties of matrices.
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Legend.
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- A, B, and C are matrices,
- O represents the zero matrix,
- I represents the identity matrix,
- r, s, and n are scalars.
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Basic.
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-A == (-1) A
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equation 1
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A - B == A + (-B)
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equation 2
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1 A = A
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equation 3
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0 A = O
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equation 4
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A + O = O + A = A
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equation 5
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I A = A I = A
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equation 6
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A - A = O
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equation 7
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Addition and scalar product.
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A + B = B + A
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equation 8
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(A + B) + C = A + (B + C)
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equation 9
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r (A + B) = r A + r B
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equation 10
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(r + s) A = r A + s A
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equation 11
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(r s) A = r (s A)
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equation 12
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Matrix product.
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A0 == I
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equation 13
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A2 == A A
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equation 14
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An = A An - 1
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equation 15
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(A B) C = A (B C)
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equation 16
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A (B + C) = A B + A C
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equation 17
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(A + B) C = A C + B C
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equation 18
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Transpose and inverse.
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IT = I
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equation 19
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(AT)T = A
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equation 20
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(A + B)T = AT + BT
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equation 21
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(r A)T = r AT
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equation 22
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(A B)T = BT AT
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equation 23
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I-1 = I
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equation 24
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A A-1 = A-1 A = I
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equation 25
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(A B)-1 = B-1 A-1
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equation 26
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(A-1)T = (AT)-1
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equation 27
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Trace.
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tr (A + B) = tr A + tr B
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equation 28
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tr (r A) = r tr A
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equation 29
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tr (A B) = tr (B A)
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equation 30
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Determinant and adjoint.
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det O = 0
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equation 31
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det I = 1
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equation 32
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det A = det AT
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equation 33
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det (A B) = (det A) (det B)
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equation 34
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A (adj A) = (adj A) A = (det A) I
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equation 35
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Navigation.
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Erik Max Francis
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Reference
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-- UP
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Mathematics reference: Rules for vectors
-- PREVIOUS
Basic properties of vectors.
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-- PERSONAL
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-- COPYRIGHT
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Copyright © 2025 Erik Max Francis. All rights reserved.
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