Indexing

• 1-based indexing — first element is A(1), not A(0)
• end keyword for last index — A(end), A(end-1), works in any dimension
• Linear indexing on matrices — A(5) accesses 5th element column-major order
• Logical indexing returns vector — A(A > 0) gives 1D result regardless of A's shape

Matrix vs Element-wise

• * is matrix multiplication — .* for element-wise
• / solves A*x = B — ./ for element-wise division
• ^ is matrix power — .^ for element-wise power
• Forgetting the dot is silent bug — dimensions might accidentally match

Vector Shape Matters

• Row vector: [1 2 3] or [1, 2, 3] — shape is 1×3
• Column vector: [1; 2; 3] — shape is 3×1
• Transpose with ' (conjugate) or .' (non-conjugate) — for complex, they differ
• * between row and column gives scalar or matrix — depending on order

Array Preallocation

• Growing arrays in loops is slow — preallocate: A = zeros(1000, 1)
• zeros, ones, nan for preallocation — specify size upfront
• Cell arrays: cell(n, m) — preallocate cells too

Broadcasting

• Implicit expansion since R2016b — A + b works if dimensions compatible
• Singleton dimensions expand — [1;2;3] + [10 20] gives 3×2
• Before R2016b needed bsxfun — legacy code may still use it

NaN Handling

• NaN ~= NaN is true — use isnan() to check
• Most operations propagate NaN — sum([1 NaN 3]) is NaN
• Use 'omitnan' flag — sum(A, 'omitnan'), mean(A, 'omitnan')

Cell Arrays vs Matrices

• {} for cell arrays — hold mixed types, different sizes
• () indexing returns cell — C(1) is 1×1 cell
• {} indexing extracts content — C{1} is the actual value
• Comma-separated list from C{:} — useful for function arguments

Common Mistakes

• = for assignment, == for comparison — if x = 5 is error in MATLAB
• Semicolon suppresses output — forget it and flood command window
• clear removes all variables — use clearvars for selective, close all for figures
• i and j are imaginary unit — don't use as loop variables, or reassign explicitly
• String vs char: "text" vs 'text' — double quotes are string arrays (R2017a+)

Functions

• Anonymous functions: f = @(x) x^2 — quick inline functions
• Multiple outputs: [a, b] = func() — must capture or use ~ to ignore
• nargin/nargout for optional args — check how many inputs/outputs provided
• varargin/varargout for variable args — cell array of extra arguments

Debugging

• dbstop if error — breakpoint on any error
• keyboard in code pauses execution — enter debug mode at that line
• whos shows variable sizes — size(A) for specific variable