Notes in Strang, Gilbert; Introduction to Linear Algebra (2016)

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Status	Last Update	Fields
Published	07/25/2023	Dot product (algebraic)
Published	07/18/2023	The dot product is also called the _______ product.
Published	07/18/2023	Dot product (geometric definition)
Published	07/18/2023	The dot product is _____ when the vectors are perpendicular.
Published	07/18/2023	Dot product (intuitive definition)
Published	07/18/2023	The length \(\lVert v \rVert\) of a vector \(v\) (in terms of a dot product)
Published	07/18/2023	The length of a unit vector
Published	07/18/2023	\(u \cdot u\), where \(u\) is a unit vector
Published	07/18/2023	The standard unit vector along the x-axis (in two dimensions)
Published	07/18/2023	The standard unit vector along the y-axis (in 2 dimensions)
Published	07/18/2023	The unit vector that makes an angle \(\theta\) with the x-axis (in two dimensions)
Published	07/18/2023	The unit vector \(u\) in the same direction as \(v\)
Published	07/26/2023	For perpendicular vectors, \(\lVert v \rVert^2 + \lVert w \rVert^2 = \mathord{?}\)
Published	07/18/2023	The zero vector is _______ to every vector \(w\).
Published	07/19/2023	The angle between two vectors \(v\) and \(w\) is less than 90 when \(v \cdot w\) is _______.
Published	07/19/2023	The angle between the vectors \(v\) and \(w\) is greater than 90 when \(v \cdot w\) is _______.
Published	07/18/2023	Unit vectors \(u\) and \(U\) at angle \(\theta\) have \(u \cdot U = \mathord{?}\). What is the range of \(u \cdot U…
Published	07/26/2023	Cosine formula (in terms of a dot product)
Published	07/18/2023	Cauchy-Schwarz inequality
Published	07/18/2023	Triangle inequality
Published	07/19/2023	Which area contains the vectors \(cv + dw\) where \(c + d = 1\)?
Published	07/19/2023	Which area contains the vectors \(cv + dw\) where \(c = d\)?
Published	07/19/2023	Which area contains the vectors \(cv + dw\) where \(0 \leq c \leq 1\) and \(0 \leq d \leq 1\)?
Published	07/19/2023	Which area contains the vectors \(cv + dw\) where \(c \geq 0\) and \(d \geq 0\)?
Published	07/19/2023	Locate \(\frac{1}{3} u + \frac{1}{3} v + \frac{1}{3} w\) in the figure below.
Published	07/19/2023	Under what restrictions on \(c, d, e\) will the combinations \(cu + dv + ew\) fill in the dashed triangle?
Published	07/19/2023	Is the vector \(\frac{1}{2} u + \frac{1}{2} v + \frac{1}{2} w\) inside or outside the pyramid formed by \(u\), \(v\), and \(w…
Published	07/19/2023	Is there any vector that can't be produced from \(cu + dv + ew\)?
Published	07/18/2023	Which vectors (in three-dimensional space) are combinations of \(u\) and \(v\), and also combinations of \(v\) and \(w\)…
Published	07/18/2023	An \(n\)-dimensional unit cube has _____ corners.
Published	07/19/2023	An \(n\)-dimensional unit cube has _____ edges.
Published	07/19/2023	An \(n\)-dimensional unit cube has _____ \((n-1)\)-dimensional faces.
Published	07/18/2023	When a matrix is singular (not invertible), its columns are ______. This implies that \(Ax=0\) has ______ solution(s).
Published	07/25/2023	\(A\) matrix is invertible when its columns are _______. This implies \(Ax=0\) has _______ solution(s).
Published	07/25/2023	\(3 \times 3\) difference matrix
Published	07/19/2023	Geometric interpretation of (in)dependence of the columns of a \(3 \times 3\) matrix.
Published	07/25/2023	Two ways to think about matrix times vector
Published	07/25/2023	What can we say about the solutions of \(Cx=b\) when \(b=0\) and when \(b\ne 0\) where \(C\) is a \(3 \ti…
New Card	07/19/2023	Which area contains the vectors \(cv + dw\) where \(c + d = 1\) and \(c\ge0\) and \(d\ge0\)?
Published	07/26/2023	When are the two sides of the Cauchy-Schwarz Inequality (\(\| u \cdot v \| \leq \lVert u \rVert \lVert v \rVert\)) equal?
Status	Last Update	Fields