Linear Algebra Terminology

noun an impressive display or range of a particular type of thing

verb to display or arrange in a particular way

• The scientist conducted a study using a vast array of data.
• There's a whole bunch of options to choose from in that array.
• The party had an array of snacks for everyone to munch on.
• Her emotions were like an array of colors, constantly changing and unpredictable.

noun a factor that decisively affects the nature or outcome of something

adjective determining or having the power to determine an outcome

• The determinant of a matrix is a value that can be computed from its elements.
• The determinant basically tells you if a matrix can be inverted or not.
• The determinant is like the magic number that helps you solve matrix problems.
• In life, your attitude can be a determinant of your success.

noun a linear transformation that preserves the dot product of vectors

adjective relating to or involving right angles; perpendicular

• In mathematics, two vectors are orthogonal if their dot product is zero.
• The two lines are orthogonal to each other, meaning they intersect at right angles.
• I don't get why they're making us learn about orthogonal matrices in class.
• His views on politics are completely orthogonal to mine, we never seem to agree on anything.

noun a person who assists or helps someone else in a particular task or role

adjective pertaining to being next to or adjacent to something else

• The adjoint operator is a fundamental concept in functional analysis.
• The math professor talked about the adjoint in class today.
• I have no idea what the adjoint thing is all about.
• In a way, the adjoint can be seen as the 'opposite' of the original operator.

adverb in a manner that is related to or resembling an affine transformation

• The concept of transforming shapes affinely is a fundamental topic in geometry.
• She explained how to affinely transform the image using a simple example.
• Let's affinely tweak the design to make it more appealing.
• His leadership style can be described as affinely guiding his team towards success.