Linear Algebra
- is a mathematical discipline that deals with vectors and matrices and, more generally, with vector spaces and linear transformations
- unlike other parts of mathematics that are frequently invigorated by new ideas and unsolved problems, linear algebra is very well understood
Linear Algebra - Definition
Linear Algebra deals with (system of) linear equations such as
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𝑎1𝑥1 + … + 𝑎𝑛𝑥𝑛 = 𝑏
linear transformations such as
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(𝑥1, …, 𝑥𝑛) → 𝑎1𝑥1 + … + 𝑎𝑛𝑥𝑛
and their representations in vector spaces and through matrices
- 𝐿(𝑎𝑣̅) = 𝑎𝐿(𝑣̅)
- 𝐿(𝑣̅ + 𝑤̅) = 𝐿(𝑣̅) + 𝐿(𝑤̅)
- 𝐿([𝑥 𝑦]) = 𝐿(𝑥[1 0] + 𝑦[0 1]) = 𝑥𝐿([1 0]) + 𝑦 𝐿([0 1])
Linear Algebra can be expressed in 3 equivalent languages:
- Vector Spaces - which provide concise and coordinate-free statements
- Matrices - which are convenient for expressing concisely explicit computations
- Systems of Linear Equations - which provide more elementary formulations
Linear Algebra - Tutorials
- Gilbert Strang - Video Lectures
- 3Blue1Brown - Series
- Interactive Linear Algebra - interactive-linear-algebra-compressed.pdf
Linear Algebra - Subpages
- Linear Algebra vs Matrix Algebra
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