This is a series on vector algebra, but it hasn’t wrapped up yet. Here are the installments as of now:
Quantity – Different Kinds of Numbers: Vectors – it really all started with this post. But I didn’t know it yet at the time…
Groupings, Shopping Lists, and Vectors – part 1 – where we take off on a journey: why vector algebra might be important, and how come the traditional textbook approach sucks most of the juice out of it.
Groupings, Shopping Lists, and Vectors – part 2 – a shopping scenario as a starting point for what is essential about vectors: that you know which stuff and how much of each.
Groupings, Shopping Lists, and Vectors – part 3 – a natural notation for vectors different from that in textbooks, which we might call annotated vectors
Groupings, Shopping Lists, and Vectors – part 4 – vector addition seen as combining shopping lists or cash register receipts
Groupings, Shopping Lists, and Vectors – part 5 – vector addition as an entry point into the distributive property
Groupings, Shopping Lists, and Vectors – part 6 – extended prices: introducing inner products
Groupings, Shopping Lists, and Vectors – part 7 – various situations where inner products show up
Groupings, Shopping Lists, and Vectors – part 8 – weighted averages of test scores: matrix times a vector
Groupings, Shopping Lists, and Vectors – part 9 – matrix times a vector, shown in 3D!
Groupings, Shopping Lists, and Vectors – part 10 – matrix multiplication, starting from a shopping list
Groupings, Shopping Lists, and Vectors – part 11 – a further look at matrix multiplication
Groupings, Shopping Lists, and Vectors – part 12 – projective drawings described in terms of matrix multiplication
Groupings, Shopping Lists, and Vectors – part 13 – revisiting vectors and matrices: how do they relate?
Groupings, Shopping Lists, and Vectors – part 14 – how does this treatment compare with textbook treatments?
Groupings, Shopping Lists, and Vectors – part 15 – a look at Excel, showing extended price calculations
Groupings, Shopping Lists, and Vectors – part 16 – vector inner products, shown in Excel
Groupings, Shopping Lists, and Vectors – part 17 – showing matrix multiplication in a regular pattern using Excel
Groupings, Shopping Lists, and Vectors – part 18 – why matrices in textbooks are square. first look at solving equations
Groupings, Shopping Lists, and Vectors – part 19 – more on solving equations and square matrices
Groupings, Shopping Lists, and Vectors – part 20 – introduction to transformations, using pounds/shillings/guineas
Groupings, Shopping Lists, and Vectors – part 21 – graphing of pound/shilling/guinea situations – showing coordinate axes that are not at right angles
Groupings, Shopping Lists, and Vectors – part 22 – more graphing of pound/shilling/guinea situations
Groupings, Shopping Lists, and Vectors – part 23 – looks at linear combinations, and a geometric model for vector addition
Groupings, Shopping Lists, and Vectors – part 24 – looks at money exchange as a vector addition
