Algebra

1. Algebra

ID: 3f69489f-80bf-4b1b-8113-ab8fd5e20e33
CREATED: <2025-02-28 Fri 17:48>

[2025-02-28 Fri 17:49] – Algebra - Wikipedia

The study of generalizations of arithmetic operations.

1.1. Linear Algebra

ID: ff07df1a-5054-48af-8130-22534dde6bc0
CREATED: <2025-05-10 Sat 16:49>

[2025-05-10 Sat 16:50] – wiki

1.1.1. Eigenvector

ID: fa086b68-f270-4bab-82da-ff78844e6bb9
CREATED: <2025-05-26 Mon 19:03>
AKA: characteristic vector

[2025-05-26 Mon 19:03] – wiki

A vector that has its direction unchanged (or reversed) by a given linear transformation. an eigenvector v of a linear transformation T is scaled by a constant factor λ when the linear transformation is applied to it: Tv = λv. The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor λ (possibly negative).

  • The eigenvectors and eigenvalues of a linear transformation serve to characterize it

1.1.2. Permutation Matrix

ID: 78dd3ccc-9f07-49b3-be76-4b133af679a4
CREATED: <2025-05-26 Mon 19:28>

[2025-05-26 Mon 19:28] – wiki

Square binary matrix with exactly one entry of 1 in each row and each column, with all other entries 0.

1.1.3. Sparse Matrix

ID: e2e44287-6cdc-46fc-9ac5-cb4678831233
CREATED: <2025-05-27 Tue 20:11>

[2025-05-27 Tue 20:11] – wiki

'sparsity' of a matrix is often (# of nil elements)/(m*n)

1.1.4. Symmetric Matrix

ID: 0bfe9ad0-706c-4f7e-8ccf-27a48e7d4da8
CREATED: <2025-05-10 Sat 16:50>

[2025-05-10 Sat 16:50] – wiki

A square matrix that is equal to its transpose.

  1. Hermitian Matrix
    ID: cf6bee91-6066-493e-941b-7171381ab508
AKA: Self-adjoint Matrix
CREATED: <2025-05-10 Sat 16:51>

    A complex square matrix that is equal to its own conjugate transpose.

    • element at (i j) is equal to the complex conjugate of the element at (j i)

1.2. Abstract Algebra

ID: 8208c5b8-462c-4f11-b935-246de88e6667
CREATED: <2025-02-28 Fri 17:55>

[2025-02-28 Fri 17:56] – Abstract algebra - Wikipedia

1.2.1. Category Theory

ID: 993236b2-fc86-4cce-ac35-0730976a8333
CREATED: <2025-02-28 Fri 17:56>

[2025-02-28 Fri 17:56] – Category theory - Wikipedia

  1. Category
    ID: d94b3cbc-9dca-430f-af25-523fa12273e6
CREATED: <2025-02-28 Fri 18:06>

    [2025-02-28 Fri 18:07] – Category (mathematics) - Wikipedia

    Abstract Categories

  2. Monoidal Category
    ID: 0ebc3d0a-8913-49c1-b8a1-c62ac145b2ba
CREATED: <2025-02-28 Fri 18:08>

    [2025-02-28 Fri 18:08] – Monoidal category - Wikipedia

    1. Concrete Category
      ID: 14121452-3f4f-459f-9116-f8fdafd8cd73
CREATED: <2025-02-28 Fri 18:06>

      [2025-02-28 Fri 18:07] – Concrete category - Wikipedia

    2. Free Category
      ID: 757943f2-fe8b-4727-86d3-bcbda1dd2536
CREATED: <2025-05-18 Sun 17:07>

      [2025-05-18 Sun 17:08] – wiki

  3. Functor
    ID: d0b0d9af-ffae-42c4-a151-1f947f348077
CREATED: <2025-02-28 Fri 18:13>

    [2025-02-28 Fri 18:13] – Functor - Wikipedia

  4. Operad
    ID: eca3fc3d-22c2-474c-9966-82ce724a0607
CREATED: <2025-02-28 Fri 18:05>

    [2025-02-28 Fri 18:05] – Operad - Wikipedia

    • a structure containing:

1.2.2. Universal Algebra

ID: b7e6df5e-8393-4763-87a5-7183b62ad07e
CREATED: <2025-02-28 Fri 17:58>

[2025-02-28 Fri 17:58] – Universal algebra - Wikipedia

  1. Partial Algebra
    ID: 2054dbdf-d464-44fb-96b9-c3f41e006ca3
CREATED: <2025-02-28 Fri 18:26>

    [2025-02-28 Fri 18:26] – Partial algebra - Wikipedia

1.3. Algebraic Topology

ID: bcaa674a-b485-46db-955c-17ba5eec4592
CREATED: <2025-02-28 Fri 17:59>

[2025-02-28 Fri 17:59] – Algebraic topology - Wikipedia [2025-02-28 Fri 18:13] – Topological space - Wikipedia

1.3.1. Hausdorff Dimension

ID: 4171e0af-f048-4973-9d33-96b1f2b17548
CREATED: <2025-05-07 Wed 16:53>
AKA: Topological Dimension

[2025-05-07 Wed 16:53] – wiki

A measure of roughness, or more specifically fractal dimension introduced in 1918 by Felix Hausdorff.

  • single point = 0
  • line segment = 1
  • square = 2
  • cube = 3

1.3.2. Manifold

ID: df5c5eda-929c-4f96-bbb8-99a751eea4f6
CREATED: <2025-05-22 Thu 19:54>

[2025-05-22 Thu 19:54] – wiki

1.4. Algebraic Structure

ID: f66bf1e0-ef4f-4038-9da5-06dca676dba9
CREATED: <2025-02-28 Fri 18:10>

Algebraic structure - Wikipedia :END:

1.4.1. Ring

ID: cefe6101-7e04-451f-a69c-d831e5ddb4e1
CREATED: <2025-05-18 Sun 17:25>

[2025-05-18 Sun 17:25] – wiki

1.4.2. Group

ID: c93a7820-514e-422a-af95-1dd6f8846665
CREATED: <2025-02-28 Fri 18:29>

[2025-02-28 Fri 18:29] – Group (mathematics) - Wikipedia

1.4.3. Set

ID: 4c5eb400-b3f5-48fb-875b-f7a5f3c99ede
CREATED: <2025-02-28 Fri 18:30>

[2025-02-28 Fri 18:30] – Set (mathematics) - Wikipedia

  1. Monoid
    ID: dc5499f7-fba9-469d-9e97-14ae866d01f1
CREATED: <2025-05-18 Sun 17:10>

    [2025-05-18 Sun 17:10] – wiki

1.4.4. Magma

ID: b703c556-fd85-484e-954e-2f6f163a5752
CREATED: <2025-02-28 Fri 18:30>

[2025-02-28 Fri 18:31] – Magma (algebra) - Wikipedia

1.4.5. Function

ID: 39130a13-90fc-4e04-a05a-acdf31fc88ad
CREATED: <2025-02-28 Fri 18:31>

[2025-02-28 Fri 18:31] – Function (mathematics) - Wikipedia

  1. Inverse
    ID: 82e956dc-69e5-4eef-993f-6afa97a38312
CREATED: <2025-02-28 Fri 18:36>

    [2025-02-28 Fri 18:36] – Inverse function - Wikipedia

1.4.6. Operation

ID: feaa8203-1dfe-4009-8a12-56b3a044d183
CREATED: <2025-02-28 Fri 18:31>

[2025-02-28 Fri 18:31] – Operation (mathematics) - Wikipedia