Types: 8.8 Unit Lower-Triangular Matrix
Examples: N/A
Constructions: N/A
Generalizations: N/A
Properties: N/A
Sufficiencies: N/A
Questions: N/A
Lower-Triangular Matrix
L ∈ R n × n
Let L ∈ R n × n be a given square matrix. We say L is lower-triangular iff entry ℓ i k = 0 for all i < k . Lower-triangular matrices take the form
L = [ ℓ 11 0 … 0 ℓ 21 ℓ 22 ⋱ ⋮ ⋮ ⋱ ⋱ 0 ℓ n 1 ℓ n 2 … ℓ n n ]
The lower-triangular entries of a matrix A are all 8.2 Entries of a Matrix on or below the main diagonal. Thus, we say that element a i k is a lower-triangular entry if and only if i ≥ k .
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5e91140120203329ae2ab974f6f69323a1d35949: I n = [ 1 0 … 0 0 1 ⋱ ⋮ ⋮ ⋱ ⋱ 0 0 … 0 1 ]
03eb0ce7e91b85f44a7db2cfdff93cc5b71bfbbe: [ a 11 a 12 a 13 a 14 a 15 a 16 a 21 a 22 a 23 a 24 a 25 a 26 a 31 a 32 a 33 a 34 a 35 a 36 a 41 a 42 a 43 a 44 a 45 a 46 a 51 a 52 a 53 a 54 a 55 a 56 a 61 a 62 a 63 a 64 a 65 a 66 ]
2ca0bf9a1ed80d80f413a177c95f1e7e1e170d0b: [ a 11 a 12 a 13 a 14 a 15 a 16 a 21 a 22 a 23 a 24 a 25 a 26 a 31 a 32 a 33 a 34 a 35 a 36 a 41 a 42 a 43 a 44 a 45 a 46 a 51 a 52 a 53 a 54 a 55 a 56 a 61 a 62 a 63 a 64 a 65 a 66 ]
376bc28ac2eb8c3d2cc49152918b541f9172db4e: [ a 11 a 12 a 13 a 14 a 15 a 16 a 21 a 22 a 23 a 24 a 25 a 26 a 31 a 32 a 33 a 34 a 35 a 36 a 41 a 42 a 43 a 44 a 45 a 46 a 51 a 52 a 53 a 54 a 55 a 56 a 61 a 62 a 63 a 64 a 65 a 66 ]
79faa457317a00c9b18ba0ed1a2fa93e8241d467: [ a 11 a 12 a 13 a 14 a 15 a 16 a 21 a 22 a 23 a 24 a 25 a 26 a 31 a 32 a 33 a 34 a 35 a 36 a 41 a 42 a 43 a 44 a 45 a 46 a 51 a 52 a 53 a 54 a 55 a 56 a 61 a 62 a 63 a 64 a 65 a 66 ]
9e5e9c1128ca168e0329e9107ff78420f83067d5: [ a 11 a 12 a 13 a 14 a 15 a 16 a 21 a 22 a 23 a 24 a 25 a 26 a 31 a 32 a 33 a 34 a 35 a 36 a 41 a 42 a 43 a 44 a 45 a 46 a 51 a 52 a 53 a 54 a 55 a 56 a 61 a 62 a 63 a 64 a 65 a 66 ]
The strictly lower-triangular entries of a matrix are all entries a i k with i > k .
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Text Elements
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5e91140120203329ae2ab974f6f69323a1d35949: I n = [ 1 0 … 0 0 1 ⋱ ⋮ ⋮ ⋱ ⋱ 0 0 … 0 1 ]
03eb0ce7e91b85f44a7db2cfdff93cc5b71bfbbe: [ a 11 a 12 a 13 a 14 a 15 a 16 a 21 a 22 a 23 a 24 a 25 a 26 a 31 a 32 a 33 a 34 a 35 a 36 a 41 a 42 a 43 a 44 a 45 a 46 a 51 a 52 a 53 a 54 a 55 a 56 a 61 a 62 a 63 a 64 a 65 a 66 ]
2ca0bf9a1ed80d80f413a177c95f1e7e1e170d0b: [ a 11 a 12 a 13 a 14 a 15 a 16 a 21 a 22 a 23 a 24 a 25 a 26 a 31 a 32 a 33 a 34 a 35 a 36 a 41 a 42 a 43 a 44 a 45 a 46 a 51 a 52 a 53 a 54 a 55 a 56 a 61 a 62 a 63 a 64 a 65 a 66 ]
376bc28ac2eb8c3d2cc49152918b541f9172db4e: [ a 11 a 12 a 13 a 14 a 15 a 16 a 21 a 22 a 23 a 24 a 25 a 26 a 31 a 32 a 33 a 34 a 35 a 36 a 41 a 42 a 43 a 44 a 45 a 46 a 51 a 52 a 53 a 54 a 55 a 56 a 61 a 62 a 63 a 64 a 65 a 66 ]
79faa457317a00c9b18ba0ed1a2fa93e8241d467: [ a 11 a 12 a 13 a 14 a 15 a 16 a 21 a 22 a 23 a 24 a 25 a 26 a 31 a 32 a 33 a 34 a 35 a 36 a 41 a 42 a 43 a 44 a 45 a 46 a 51 a 52 a 53 a 54 a 55 a 56 a 61 a 62 a 63 a 64 a 65 a 66 ]
9e5e9c1128ca168e0329e9107ff78420f83067d5: [ a 11 a 12 a 13 a 14 a 15 a 16 a 21 a 22 a 23 a 24 a 25 a 26 a 31 a 32 a 33 a 34 a 35 a 36 a 41 a 42 a 43 a 44 a 45 a 46 a 51 a 52 a 53 a 54 a 55 a 56 a 61 a 62 a 63 a 64 a 65 a 66 ]